Gestion de données, fonctions
Fonction linéaire, fonction affine, proportionnalité
None
Multiple examples of constructing linear equations in slopeintercept form
Linear Equations in Slope Intercept Form
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At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?

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I don't understand why we divide by three at about 7:50. help?
He is basically simplifying the problem 5/6 multiplied by 3/1, 3 and 6 both are divisible by 3 so he simplifies the equation making it 5/2 multiplied by 1 which then results in 5/2
At 7:50 he is multiplying 5/6 by 3 which is the same as 3/1. So if you multiply the numerators you would get 15 and when you multiply the denominators you get 6. Hence you are left with 15/6 which is not simplified. Because the numerator and denominator are both divisible by three he divides them by three to simplify the fraction and he gets 5/2
I just learned this in math but you divide the number by 3 because as seen above it shows...
"05 over 33. This means that it equals 5/6=5/6. 5 and 5 would go to 1=1 and 6=6 would simplify to 3=1. SO that is what he means as divide by 3. :)
"05 over 33. This means that it equals 5/6=5/6. 5 and 5 would go to 1=1 and 6=6 would simplify to 3=1. SO that is what he means as divide by 3. :)
that makes no sense
how do you change from pointslope form to slopeintercept?
y  y1 = m(x  x1)
=> y  y1 = mx  mx1
=> y = mx  mx1 + y1
then simplify.
With an example containing actual numbers, you see it's much easier than the steps above imply:
y  7 = 4(x  2)
=> y  7 = 4x  8
=> y = 4x  8 + 7
=> y = 4x  1
Additional resource: http://www.mathwarehouse.com/algebra/linear_equation/pointslopetoslopeinterceptform.php
=> y  y1 = mx  mx1
=> y = mx  mx1 + y1
then simplify.
With an example containing actual numbers, you see it's much easier than the steps above imply:
y  7 = 4(x  2)
=> y  7 = 4x  8
=> y = 4x  8 + 7
=> y = 4x  1
Additional resource: http://www.mathwarehouse.com/algebra/linear_equation/pointslopetoslopeinterceptform.php
yy1=m(xx1).....this is the point slope form
yy1=x(m)+x1(m)....you distribute the m
y=xm+x1(m)+y1.....you move the y1 to the other side
and then simplify
ex:y+1=1/2(x+6)....this is the point slope form
y+1=1/2x3
y=1/2x3+2
y=1/2x1....that is the slope intercept form
yy1=x(m)+x1(m)....you distribute the m
y=xm+x1(m)+y1.....you move the y1 to the other side
and then simplify
ex:y+1=1/2(x+6)....this is the point slope form
y+1=1/2x3
y=1/2x3+2
y=1/2x1....that is the slope intercept form
the formula for pointslope form is yy1=m(xx1) if you had a slope of 3, and a point on the line that was (1,2) it would look like y2=3(x1) which would simplify to y2=3x3 you add 2 to both sides and it becomes: y=3x5
Why do we use X as the common variable in algebra? X is also the horizontal axis in graphs.
That's not a coincidence, as you will see when you start graphing algebraic equations.
The whole point of equations are to graph a line and show a relationship between two of more values so x is one of the values that you a showing a relationship to
I think x, y, and z are all common variables, but the first letter(x) seems to be used a lot in algebraic equations.
When you start graphing you will understand
Thanks a lot guys..
Wouldn't they be mistaken for each other?
What is the difference between f(x) and y? Sal said that he assumed they were equal, but can there be cases where they aren't? How would that work?
They're the same thing, but in higher math classes you use f(x) because you graph functions and y can be used as a variable. Say you have a question that says
f(x)=3x + 4, what is f(2), you would simply plug in 2 for x and get 10. It's much more useful in more advanced math.
You can also watch this video.
https://www.khanacademy.org/math/cceighthgrademath/cc8threlationshipsfunctions/cc8thfunctionnotation/v/differencebetweenequationsandfunctions
At first when you are learning functions, you would think that they are silly and you can use y instead. But later on, you will realize that y is silly.
I hope this helps!
f(x)=3x + 4, what is f(2), you would simply plug in 2 for x and get 10. It's much more useful in more advanced math.
You can also watch this video.
https://www.khanacademy.org/math/cceighthgrademath/cc8threlationshipsfunctions/cc8thfunctionnotation/v/differencebetweenequationsandfunctions
At first when you are learning functions, you would think that they are silly and you can use y instead. But later on, you will realize that y is silly.
I hope this helps!
it is just wrong
at 3:27 shoudnt it be y2y1 over x2x1 instead of y1y2 over x1x2
Believe it or not, they are the same thing. Try it.
Why is 6/3 equal to 6/3 or 2?
6/3 means 6 ÷ 3
A positive divided by a negative is a negative, and 6 ÷ 3 = 2.
Therefore 6/3 = 2
6/3 means 6 ÷ 3
A negative divided by a positive is a negative, and 6 ÷ 3 = 2
Therefore 6/3 = 2
2 = 2
Since 6/3 = 2, 6/3=2, and 2=2 (i.e. they are all equal to the same thing), they must also be equal to each other.
This same process could be done for any numbers meaning that
(x)/y = x/(y) = (x/y)
or in words: A negative in a fraction can go in front, in the numerator, or in the denominator, but not both.
A positive divided by a negative is a negative, and 6 ÷ 3 = 2.
Therefore 6/3 = 2
6/3 means 6 ÷ 3
A negative divided by a positive is a negative, and 6 ÷ 3 = 2
Therefore 6/3 = 2
2 = 2
Since 6/3 = 2, 6/3=2, and 2=2 (i.e. they are all equal to the same thing), they must also be equal to each other.
This same process could be done for any numbers meaning that
(x)/y = x/(y) = (x/y)
or in words: A negative in a fraction can go in front, in the numerator, or in the denominator, but not both.
When you simplify it you'll get 2 on both of them
At 8:37, if b in the equation y = mx+b is 5/2 or 5 halves, how would it be plotted on the coordinate plane in fraction form as the y intercept? Isn't the y intercept supposed to be a whole number, so that it can be plotted on the coordinate plane?
The yintercept can be any number, it need not be a whole number (usually is not). You just plot 2.5 as best you can, halfway between 2 and 3.
to find the slope sal subtracts (at 3:00) 60/25. check. next problem i paused, tried to figure it out myself and subtracted (at 5:54) 50/3(3) to find the slope. sal however reversed the order and did 05/33. we ended up with very different answers. how do i know which point to subtract from which point? he did them in two different orders.
Ramona, it looks like you are on the right track. Continuing from your set up, you should get this result:
slope = (50)/(3(3)) = 5/(3+3) = 5/6
That's the same answer Sal got to in the video.
To answer your question about knowing which point to subtract from which point  either way is correct! It is _your choice_ which is the 'first' point and which is the 'second'  just make sure you make the _same_ choice for both the x and y coordinates. In the video, Sal chose to set up the calculation 'green minus orange' and you set it up 'orange minus green'. But either way, once all the arithmetic is done, you should have the same answer. (Why? Note what happens at 7:01: _"...the negatives cancel out."_
slope = (50)/(3(3)) = 5/(3+3) = 5/6
That's the same answer Sal got to in the video.
To answer your question about knowing which point to subtract from which point  either way is correct! It is _your choice_ which is the 'first' point and which is the 'second'  just make sure you make the _same_ choice for both the x and y coordinates. In the video, Sal chose to set up the calculation 'green minus orange' and you set it up 'orange minus green'. But either way, once all the arithmetic is done, you should have the same answer. (Why? Note what happens at 7:01: _"...the negatives cancel out."_
This isn't exactly related to the topic, but why does 60/25 become 6/3 ?
Why isn't it just 6/3 ? I never understood this and it always stuffs me up.
Why isn't it just 6/3 ? I never understood this and it always stuffs me up.
Tomm0,
Your mistake is that (60) is +6, not 6
If you had a line that included the points (6,2) and (0,5), the slope would be (change in y)/(change in x) which would be (60)/25)
(60) is +6 , not 6
(25) is 3
So the fraction is 6/3
which reduces to 2/1 = 2
I hope that helps make it click for you.
Your mistake is that (60) is +6, not 6
If you had a line that included the points (6,2) and (0,5), the slope would be (change in y)/(change in x) which would be (60)/25)
(60) is +6 , not 6
(25) is 3
So the fraction is 6/3
which reduces to 2/1 = 2
I hope that helps make it click for you.
u need to respect the man he is smart and he is also human so are you so treat everyone the way u want to be treated
How Would You Work This Type Of Problem When It's Set Up In A Table???
do you mean if its like
x2/3/4/5/6
y4/6/8/10/12 you have to find a pattern (in this case y is twice the amount of x) so y=2x
x2/3/4/5/6
y4/6/8/10/12 you have to find a pattern (in this case y is twice the amount of x) so y=2x
Choose any two points, then find slope the same way you did without the table. After you find your slope, plug any one of the points back into y = mx + b and solve for b.
X  Y
1  3
2  5
3  7
Points (1,3),(2,5),(3,7)
Using the points (1,3) and (2,5)
m = variation in y / variation in x = 3  5 / 1  2 = 2 / 1 = 2
y = mx + b
y = 2x + b
Using the point (1,3)
(3) = 2 . (1) + b
Subtracting 2 on both sides:
b = 1
So the equation for this line is:
y = 2x + 1
1  3
2  5
3  7
Points (1,3),(2,5),(3,7)
Using the points (1,3) and (2,5)
m = variation in y / variation in x = 3  5 / 1  2 = 2 / 1 = 2
y = mx + b
y = 2x + b
Using the point (1,3)
(3) = 2 . (1) + b
Subtracting 2 on both sides:
b = 1
So the equation for this line is:
y = 2x + 1
there is always a slope #
I don't get it. At 3:39 is confusing. Why can't we use the slope equation to get the slope and then the slope would be 2 not 2. Am I missing something? He said if it's switch then it would be be negative?
I think I understand what you are trying to say, if you are talking about the equation y2y1/x2x1. So you would have 06/52. First, if we think about it, the slope will be the same no matter if it is from (2,6) to (5,0) or (5,0) to (2,6). Just know the slope is the same, so we can do it Sal's way of 60/25 or the way 06/52. You probably thought that 06 was just 6, but 06 is 6. Then you get 52 which is 3, so 6/3. If you thought 06 was 6, you would have got 2 as the slope. I think that is what you are asking
Comment if you get it or if you meant something else
Comment if you get it or if you meant something else
OMG that is what I meant! Thank you! I forgot that the number would be negative 6. I can't believe I didn't see it!
write th equation of the line in slope intercept form if the slope is 1/5 and the yintercept is 9
when you put an equation in y intercept form you always start with y= the slope goes with the x and the intercept is the next term.
y = mx +b
m is the slope, b is the intercept
y= 1/5x 9
y = mx +b
m is the slope, b is the intercept
y= 1/5x 9
What if the slope is undefined, but you are given a point. What do you do?
Hannah,
If you have a linear equation where the slope is undefined, then the denominator of the slope must be 0 since anything divided by 0 is undefined.
The denominator of the slope is the change in x
So the change in x is zero.
So if your point was (1,3) and the slope is undefined, you know that some other point has a change in y but x changes by zero,
So x would always by 1.
Points (1,3), (1,4), (1,5) would all be on your line.
The equation of this line is x=1+0y or x=1
If you graphed it you would have a vertical line. going through the x axis at the point given as the x value in your original point.
I hope that makes it click for you.
If you have a linear equation where the slope is undefined, then the denominator of the slope must be 0 since anything divided by 0 is undefined.
The denominator of the slope is the change in x
So the change in x is zero.
So if your point was (1,3) and the slope is undefined, you know that some other point has a change in y but x changes by zero,
So x would always by 1.
Points (1,3), (1,4), (1,5) would all be on your line.
The equation of this line is x=1+0y or x=1
If you graphed it you would have a vertical line. going through the x axis at the point given as the x value in your original point.
I hope that makes it click for you.
what do i do when the equation is Y = X
it means that whatever your X value is,that will also be your Y value. when X=1 Y=1 when X=5 Y=5.and therefore the slope is 1(1/1). it follows the usual equation of a line Y=mX + b.when X is 0 so is Y, that's why the Y intercept (b) isn't in the equation, its 0.
AT 2:23 I don't get how he got x
Try watching the video again.
i agree watch the video again
How do I write the slopeintercept form of the equation of the line through: (3,2), if the slope is undefined?
Hi,
If a slope is undefined, it means that the x value does not change. Remember that slope is calculated as the change in the y value divided by the change in the x value. If x does not change, then we are dividing by zero, which is undefined. Therefore, an undefined slope is a vertical line through the point you were given.
You cannot really write it in a correct slope/intercept form. Usually this is written as:
x=whatever the x value of your point is.
In your case, the equation would be
x=3
And the graph would be a vertical line running through the 3 on the x axis.
Hope that helps :)
If a slope is undefined, it means that the x value does not change. Remember that slope is calculated as the change in the y value divided by the change in the x value. If x does not change, then we are dividing by zero, which is undefined. Therefore, an undefined slope is a vertical line through the point you were given.
You cannot really write it in a correct slope/intercept form. Usually this is written as:
x=whatever the x value of your point is.
In your case, the equation would be
x=3
And the graph would be a vertical line running through the 3 on the x axis.
Hope that helps :)
I didn't understand the equation f(1.5)=3,f(1)=2?
This is because our function here is
*f(`x`)=(`x`)2*
So each time we put in a value of `x` we multiply it by 2
Ex.
f(`1.5`)=(`1.5`)*2=3
f(`1`)=(`1`)*2=2
*f(`x`)=(`x`)2*
So each time we put in a value of `x` we multiply it by 2
Ex.
f(`1.5`)=(`1.5`)*2=3
f(`1`)=(`1`)*2=2
how do you find a y intercept in a graph
i don't understand what is going on when you have to solve for b, can i please have some help?
When solving for b we put the values (x,y) of the given point (which sit on the line) in the the equation of the line in its general form: y=mx+b, where m is our slope (in this example 1) Than we separate b on one side of the equation and numbers on another.
how is it " m=delta y over delta x? " why is it not delta x over delta y?
slope can also be though of in terms of rise over run. since delta y is how far the graph is rising and delta x is how far the graph "runs", thats why the slope is delta y over delta x. It is just a mathematical convention that slope is measured that way.
muchos gracias
Is it m=y2y1 over x2x1 or m=y1y2 over x1x2? I need help. Please and Thank You.
It really doesn't matter. As long as you have the y's over the x's, you'll get the slope of your line. In fact, the two ratios are equal anyways because y1y2=(y2y1), annd the same for the x's, so multiply one way by 1/1, and you'll get the other.
It doesn't matter! Both end up with the same thing  try it. An example: (35) / (27) = 2 / 5 = 2/5. Or (53) / (72) = 2/5.
Okay thank you
About the substitution of the points. What if you don't have a zero? Do you just go with the points that are closest to one?
@ 1:07} Do you have to use m to represent the slope or do you choose any variable?
Well technically, you have to use m to represent the slope or else it wouldn't be right.
How do you make it easier to convert from a problem such as 5x + 2y = 6 without getting confused over negative numbers?
Tommy,
Typically to isolate y (so you can get into the form y = mx + b) you would start this problem by adding 5x to both sides (to get rid of the 5x on the left). This first step would give you:
2y = 5x + 6
Bingo. Your negative sign is gone. Now a you divide both sides by 2:
y = 5/2x + 3 ... and you're done!
Typically to isolate y (so you can get into the form y = mx + b) you would start this problem by adding 5x to both sides (to get rid of the 5x on the left). This first step would give you:
2y = 5x + 6
Bingo. Your negative sign is gone. Now a you divide both sides by 2:
y = 5/2x + 3 ... and you're done!
at 3:53 , why does Sal put a negative when 6  0 is not negative?
because he went the other way around just to prove you would get the same value for the slope.
how do i find an equation of the slope line?
I do not get your question.
it is y1 y2 over x1 x2
it is y1 y2 over x1 x2
( y₁ y₂)/( x₁ x₂) is the formula for slope.
to find the equation of a line sub (x,y) of a line into y=mx+b form
solve to find b
and write down the equation of the line
to find the equation of a line sub (x,y) of a line into y=mx+b form
solve to find b
and write down the equation of the line
How do you solve a problem when it asks you, " Write the equation that describes each line in slopeintercept form." and the problem is [slope= 2/7, (14,3) is on the line]? PLEASE ANSWER SOON OR PUT A VIDEO UP ON KHAN ACADEMY ABOUT MY QUESTION!!!!!!!
well look at it this way: slope= 2/7, (14,3), look at in the video 10: 11 through the rest of the video, I hoped this helped you Sophia.
And when graphing these can if you can switch the 6/3 around will it change the graph points
Stephanie,
If I understand your question correctly, you are asking how to find slope. If you are given points, (example: 1,2, 3,4) then you can find your slope using the equation:
Y2  Y1 over X2X1.
In this case, Y2 is 4 because this is the second y in the two points, Y1 is 2, X2 is 3, and X1 is 1. We now have: 42 over 31 which is 2 over 2 which can be simplified to 1. The slope of the equation is 1.
Hope this helped!
If I understand your question correctly, you are asking how to find slope. If you are given points, (example: 1,2, 3,4) then you can find your slope using the equation:
Y2  Y1 over X2X1.
In this case, Y2 is 4 because this is the second y in the two points, Y1 is 2, X2 is 3, and X1 is 1. We now have: 42 over 31 which is 2 over 2 which can be simplified to 1. The slope of the equation is 1.
Hope this helped!
Isn't 21=3 ? Sal said that it equals to 2?!
The answer is not 2. Probably just a simple mistake
The answer is negative three.
2 + 1= 3
It's the same as 2 1= 3
2 + 1= 3
It's the same as 2 1= 3
Yeah sorry I meant 3 but he said 2.
if you have 2lbs of jellybeans for $9, what of .5 lbs? 3lbs? 4 lbs?
I would solve this using proportions: if you have the proportion $9 per 2 lbs., you can divide both by 2 to get $4.50 for 1 lb. From here you can multiply both by 3, 4, or 1/2 to get your answers. I'll leave that up to you ;D
Ok, I'm bringing this up because I have noticed this over the past year.
I mean no offense, I merely want to have help!
The videos that are supposed to provide "help" are often confusing to me, and ultimately cover things I already know, and/or just confuse me further. They, in the long run, don't actually clarify the work I am supposed to do, and this frustrates me.
Is there anything that can be done about this?
Please help!!
Thank you!!
 Grace
I mean no offense, I merely want to have help!
The videos that are supposed to provide "help" are often confusing to me, and ultimately cover things I already know, and/or just confuse me further. They, in the long run, don't actually clarify the work I am supposed to do, and this frustrates me.
Is there anything that can be done about this?
Please help!!
Thank you!!
 Grace
what is the *slopeintercept formula*
and x and y are points on the graph.
y=mx+b
m is the slope and b is the yintercept.
m is the slope and b is the yintercept.
the formula is y=mx+b
at 1:48 how did he find the yintercept of the equation if it was not written in standard form ?
He knew that line goes through the point `(4/5, 0)`, right? `4/5` is an `x` value and `0` is an `y` value of this point. Also he knew that slope (m) is equal to `1`. Therefore by substituting the values to the formula of `y = mx + b` we get `0 = 1 * 4/5 + b` which is an equation with one variable and just like Sal did  `0 = 4/5 + b` therefore `b = 4/5`.
i really do not understand this video. how would you write in a equation form: Jan wants to buy maps and atlases. the maps cost $2 each and the atlases cost each $5. If she buys 3 atlases and spends $25, how many maps can she buy?
Can you plze explain how to write an equation with this example?
Can you plze explain how to write an equation with this example?
An equation for this is
t = 2m + 5a
where t = total, m = maps, a = atlases
You're also told that a = 3 and t = 25, so
25 = 2m + 5 * 3
Solve for m.
t = 2m + 5a
where t = total, m = maps, a = atlases
You're also told that a = 3 and t = 25, so
25 = 2m + 5 * 3
Solve for m.
Will you please show how to find the slopeintercept form for the line satisfying the following:
xintercept 3, yintercept 2/3?
xintercept 3, yintercept 2/3?
Well remember x represent the horizontal line and so your first point will be (3,0) while the vertical line (y) represent a point in y lower than 1 (dividing 1 in thirth so you take 2 of them and you have 2/3). Finally your second point is (0,2/3) and join the dots.
m= 3  0/0  2/3= 9/2 = 4 1/2... y= 9/2x+2/3 (mx+b)
Sorry if I was a little obvious but my intention was be clear!
m= 3  0/0  2/3= 9/2 = 4 1/2... y= 9/2x+2/3 (mx+b)
Sorry if I was a little obvious but my intention was be clear!
How do you write the the equation if its a word problem?
Write down what you know and what you don't know and what it is asking for clearly. Try to find a relationship. Remember that all lines have a slope (m), which is basically how steep it is, which is simply a measure of how far it moves along the x axis over how far it moves along the y axis, and a point of origin where it crosses a known point. In normal notation, this is the y intercept (b), which occurs when x = 0.
what is the x for ?
Its the value of the number on the x axis.
Oh yeah,  x is just a variable.
Oh yeah,  x is just a variable.
noni la cubana, in y = mx + b, x just represents a general variable! x could be anything. That's why you keep it as x when you write an equation in "Slope Intercept Form".
Hope that helps!
Hope that helps!
If we can plot an equation in which no x is defined ( e.g. 2y=8 where we assume 0x) why can we not graph an equation in which no y is defined (e.g. 4x=8)
You can graph 4x=8. When you divide both sides by 4 you get x=2. This is simply a vertical line which crosses the x intercept at 2. That vertical line includes all points in which x is equal to 2.
You can, it is the point 2 on the x axis. If plotted in two dimensions (2,0).
Is there a particular reason why Sal used less common variables in this video? Or did he just want to through in a variety?
Well, if you are talking about him using the variables: m, x, y, and b, he is using the equation of slopeintercept form, which is *y = xm + b*. "b" is the yintercept and "m" is the slope of the line, and x + y are points on the line, of course. This equation makes a straight line. If you want to know more, just look here: https://www.khanacademy.org/math/algebra/linearequationsandinequalitie/equationofaline/v/graphingalineinslopeinterceptform.
Also, the f at around 10:32 is a symbol for function.
Also, the f at around 10:32 is a symbol for function.
at 2:57 in the videos sal used these triangular shaped things in the equation what are they and what do they represent
They are the Greek symbol delta. They are accepted in math and science as the word "change".
thanks for telling me what they ment cause i started to get a bit skeptical about them.
How do you write an equation in slope intercept form?
A linear equation in slopeintercept form is y = mx + b. Where "m" is your slope and "b" is your yintercept.
The yintercept would be zero and the slope would be 1.It would have a constant increase and go in a straight equal line.
Hi you have done that in a problem
Line contain points (2,6) and (5,0)
m=y1y2/x1x2
but the formula is
http://cs.selu.edu/~rbyrd/math/slope/slo_eq1.gif
Line contain points (2,6) and (5,0)
m=y1y2/x1x2
but the formula is
http://cs.selu.edu/~rbyrd/math/slope/slo_eq1.gif
Since (x1,y1) and (x2,y2) could be either of the two points, it it true that is doesn't matter which way the slope formula is written. It is important that you use your original point for both the numerator and denominator or your slope will have the opposite sign it should have.
It doesn't matter if its y1y2 or y2y1
Around 4:12, Sal had a problem which said,
"The line contains points (2,6) and (5,0)"
In this problem, Sal subtracts this way, "60/25"
In the next problem 6:48 Sal does his problem "The line contains points (3,5) and (3,0)" and SWITCHES AROUND compared to his problem before, by subtracting "05/3  3".
I'm not a mathematical genius compared to Sal so please help me see where I'm going wrong. I thought the problem would turn out like this,
"50/ 33"
Sal's Equation: "05/ 3 3"
"The line contains points (2,6) and (5,0)"
In this problem, Sal subtracts this way, "60/25"
In the next problem 6:48 Sal does his problem "The line contains points (3,5) and (3,0)" and SWITCHES AROUND compared to his problem before, by subtracting "05/3  3".
I'm not a mathematical genius compared to Sal so please help me see where I'm going wrong. I thought the problem would turn out like this,
"50/ 33"
Sal's Equation: "05/ 3 3"
Christian, that's ok! You see, when you want to do these problems, you usually have two sets of points, right? Let's call them (X1,Y1) and (X2, Y2). Now, in school, usually the general formula taught for finding slope is (Y2  Y1) divided by (X2  X1). But, as you'll learn later on (if you aren't taking higher level math yet) that the equation is actually "CHANGE OVER Y" divided by "CHANGE OVER X". The order in which you subtract doesn't matter, as long as you subtract the Ys and divide them by the subtraction of the Xs. If you'll notice, your equation gives you the answer "5/6," which is "5/6". Sal's answer is also "5/6".
Hope that helps!
Hope that helps!
what does delta mean?
Delta is a Greek letter: http://en.wikipedia.org/wiki/Delta_(letter).
Mathematicians use the letter delta to represent a change in value of a variable. For example, ∆x is the change in the x variable. So when you see ∆y/∆x you know you're dealing with slope as it's the change in y compared to (or over) the change in x. This is also called rise over run: rise is how far you change vertically. Run is how far you change horizontally.
Mathematicians use the letter delta to represent a change in value of a variable. For example, ∆x is the change in the x variable. So when you see ∆y/∆x you know you're dealing with slope as it's the change in y compared to (or over) the change in x. This is also called rise over run: rise is how far you change vertically. Run is how far you change horizontally.
what is linear equation
Yogi,
A linear equation is an equation which graphs to form a line.
It usually takes the form of y = ax+b where a and b are constants such as y=2x+1.
When you graph it, it forms a strait line, so they call it a linear equation.
Here is a video that might help you understand more:
http://www.khanacademy.org/math/algebra/linearequationsandinequalitie/graphing_solutions2/v/algebragraphinglines1
A linear equation is an equation which graphs to form a line.
It usually takes the form of y = ax+b where a and b are constants such as y=2x+1.
When you graph it, it forms a strait line, so they call it a linear equation.
Here is a video that might help you understand more:
http://www.khanacademy.org/math/algebra/linearequationsandinequalitie/graphing_solutions2/v/algebragraphinglines1
How are you supposed to find the fraction
aka the answer?! I need help.. any1?
aka the answer?! I need help.. any1?
IM THE SHORT GUY PEOPLE PLZ HELP!.... and thx and i wonder who else needs help ..
ya but your awsner doesn´t help :P
How do i turn x+2y=5 into slope intercept form? PLEASE HELP
TCulton,
The slope intercept form is y=mx+b
You have the form x+2y=5
In the slope intercept form, the y is all by itself on the left. So convert
x+2y=5 to a from that has y by itself on the left side of the equation
x+2y=5 First get rid of the x on the left by subtracting x from both sides.
xx+2y=5x so
2y=5x Now get rid of the 2 by dividing each side by 2
2y/2 = 5/2  x/2 so
y=5/2  x/2 Now change the order on the left
y=(1/2)x+5/2
So it is now in slope yintercept form. The slope is 1/2 and the yintercept is the point (0,5/2)
The slope intercept form is y=mx+b
You have the form x+2y=5
In the slope intercept form, the y is all by itself on the left. So convert
x+2y=5 to a from that has y by itself on the left side of the equation
x+2y=5 First get rid of the x on the left by subtracting x from both sides.
xx+2y=5x so
2y=5x Now get rid of the 2 by dividing each side by 2
2y/2 = 5/2  x/2 so
y=5/2  x/2 Now change the order on the left
y=(1/2)x+5/2
So it is now in slope yintercept form. The slope is 1/2 and the yintercept is the point (0,5/2)
Subtract x from both sides
Divide both sides by 2
Done
Divide both sides by 2
Done
At 7:20 why did he choose the second point, what if the first piont??
It doesn't matter which point you select. Sal probably picked the 2nd point because the zero usually makes some of the math easier to do. If you were to use the 1st point to find "b", you would get the same value for "b". Here it is:
5 = 5/6(3) + b
5 = 15/6 + b
5 = 5/2 + b
10/2  5/2 = b
5/2 = b
5 = 5/6(3) + b
5 = 15/6 + b
5 = 5/2 + b
10/2  5/2 = b
5/2 = b
how do i make 6x  3y = 9 in slope intercept form
Isolate y:
6x  3y = 9, add 3y to both sides
6x = 9 + 3y, then add 9 to both sides
6x + 9 = 3y, then divide everything by 3
2x + 3 = y
you can always enter this kind of stuff into wolfram alpha and they will solve it and graph it for you: http://www.wolframalpha.com/
6x  3y = 9, add 3y to both sides
6x = 9 + 3y, then add 9 to both sides
6x + 9 = 3y, then divide everything by 3
2x + 3 = y
you can always enter this kind of stuff into wolfram alpha and they will solve it and graph it for you: http://www.wolframalpha.com/
how do i put 6x  3y in slop intercept form
how do i solve 6x  3y = 9 for y
check my previous answer, but be aware that the value of y depends on x. Every solution is a point that is on the line 6x  3y = 9
You need to isolate y. Right now, y has a coefficient of (3) and 6x is added to it. First, move 6x to the other side of the equation by subtracting 6x from both sides (because we're doing the same thing to both sides we're not logically changing anything, we're only rearranging).
```
6x  3y  6x = 9  6x
```
Our equation simplifies to
```
3y = 9  6x
```
because
```
6x  6x = 0
```
and we can do addition/subtraction in any order we like so it doesn't matter that they're not right next to each other). We now need to remove the coefficient of 3. Note that 3*(1/3) = 1. So if we multiply both sides by 1/3, we'll be left with just y on the left hand side.
```
y = (9  6x) * (1/3)
```
I put parentheses around the subtraction of the RHS(right hand side) because we were multiplying the entire RHS by 1/3 so it needs to be distributed over addition/subtraction terms.
```y = (9 * (1/3)  6x * (1/3))```
becomes
```y = 3  2x```
and subtracting by a negative gives us addition so the final answer is
```y = 3 + 2x```
```
6x  3y  6x = 9  6x
```
Our equation simplifies to
```
3y = 9  6x
```
because
```
6x  6x = 0
```
and we can do addition/subtraction in any order we like so it doesn't matter that they're not right next to each other). We now need to remove the coefficient of 3. Note that 3*(1/3) = 1. So if we multiply both sides by 1/3, we'll be left with just y on the left hand side.
```
y = (9  6x) * (1/3)
```
I put parentheses around the subtraction of the RHS(right hand side) because we were multiplying the entire RHS by 1/3 so it needs to be distributed over addition/subtraction terms.
```y = (9 * (1/3)  6x * (1/3))```
becomes
```y = 3  2x```
and subtracting by a negative gives us addition so the final answer is
```y = 3 + 2x```
i dont understand why negatives cancel out
A negative is the opposite of a number. The opposite of 2 is 2. The opposite of 2 is 2. Two negatives means 'the opposite of the neg. number', which is positive. Therefore 2=2. Three negatives (2) is the opposite of the opposite of the opposite of 2.
If you are not a boy, you are a girl. If you are not not a boy, you are a boy.
Why does he subtract the two points when one is greater in x and y values than the other?
Humza,
For some reason, I can't access the video right now, but what Sal was probably trying to do was to calculate the slope of the line from two points that are on the line. In order to do that, the formula is m=(y2y1)/(x2x1). Basically that means that you call one of the points, "point 1" and the other "point 2". Then you subtract point 1's y value from point 2's, and divide that by point 2's x value minus point 1's x value.
For some reason, I can't access the video right now, but what Sal was probably trying to do was to calculate the slope of the line from two points that are on the line. In order to do that, the formula is m=(y2y1)/(x2x1). Basically that means that you call one of the points, "point 1" and the other "point 2". Then you subtract point 1's y value from point 2's, and divide that by point 2's x value minus point 1's x value.
The slope is the distance between y's over the distance between x's. You can start with either point first and you always subtract the two x values and the two y values starting with the same point for both x and y.
For instance, if you had two points (1,2) and (3,6) you could find the slope using either
(26)/(13) or (62)/(31)
They solve to:
(4)/(2) OR (4)/(2)
which both equal 2.
Does that help?
For instance, if you had two points (1,2) and (3,6) you could find the slope using either
(26)/(13) or (62)/(31)
They solve to:
(4)/(2) OR (4)/(2)
which both equal 2.
Does that help?
i cant figure out what (34,87) (51,25) can u plaese help me
I know that the slope is the change in y divide by the change in x. But what are you getting, if anything, if you divided the change in x by the change in y?
George,
If you take the *negative* of change in x over change in y, you would have the slope of a line perpendicular to the original line.
This video explains why: https://www.khanacademy.org/math/algebra/linearequationsandinequalitie/moreanalyticgeometry/v/perpendicularlines
If you take the *negative* of change in x over change in y, you would have the slope of a line perpendicular to the original line.
This video explains why: https://www.khanacademy.org/math/algebra/linearequationsandinequalitie/moreanalyticgeometry/v/perpendicularlines
I thought it was y2  y1 over x2  x1.
and it is, the short way to write it like you did is just to put the little triangle before the x and the y. tha just means change!
At 3:28 why does he put the first coordinate first? the equation is y>2 y>1
x>2 x>1
x>2 x>1
You can pick either one to be honest. you can start with the first coordinates or the second coordinates it doesn't matter the order.
Hi Sirena
From Mitchell
From Mitchell
how would you determinr the the rate of change is constant for tables given.
Spencer,
If the
(change in y) / (change in x) is always the same, then the rate of change is constant.
If you table has the following
(3,5)
(4,7)
(6,11)
(7,14)
You could calculate (change in y)/(change in x)
For the first two terms (75)/43) = 2/1 = 2
The second & third term (117)/(64) = 4/2 = 2
So far the change is constant
The third and fourth term (1411)/(76) = 3/1 = 3
This last point in our table shows we have a different ratio for
(change in y)/(change in x) so the table does not have a constant rate of change.
I hope that helps make it click for you.
If the
(change in y) / (change in x) is always the same, then the rate of change is constant.
If you table has the following
(3,5)
(4,7)
(6,11)
(7,14)
You could calculate (change in y)/(change in x)
For the first two terms (75)/43) = 2/1 = 2
The second & third term (117)/(64) = 4/2 = 2
So far the change is constant
The third and fourth term (1411)/(76) = 3/1 = 3
This last point in our table shows we have a different ratio for
(change in y)/(change in x) so the table does not have a constant rate of change.
I hope that helps make it click for you.
what does f(x)  f of x mean?
f=function. If you have an equation like y = 3x + 7 then you can also say that y is a function of x, or f(x). f(x) = 3x +7.
Sal, you kept saying that the points listed MUST satisfy the equation, what if the points do not satisfy the equation, I'm just wondering?
Points that dont' satisfy the equation cannot be on the line.
If a point does not satisfy the equation, the point cannot be on the line, therefore being unnecessary.
Sorry, could someone explain to me why you multiply x by the slope?
When x increases by 1, y increases by the slope m.
Consider the points (0,b) and (x,y).
Here the first coordinate increases by x and therefore the second coordinate should increase by m times x:
y = m*x + b
Consider the points (0,b) and (x,y).
Here the first coordinate increases by x and therefore the second coordinate should increase by m times x:
y = m*x + b
When finding the slope from the points could you just stack and subtract? Would that work everytime for points?
that was the way i was taught. it never gave me any trouble before. that math is much easier to do in your head anyway and maybe only need to write one or two numbers down till you get the answer.
what if all you have are two points? how would you find the yintercept? I still don't understand!!
Two points define a line, and if you define a line, then you define the yintercept. If you have two points, you can calculate the slope of a line between them. Then you can write y = mx + b, and you know x. Plug in the y and x of one point, and solve for b. That's the y interecept.
Please explain how to graph the equation and state the slope of the line if the slope existed Example x=8
x = 8 is a vertical line, because it says no matter what the y value is, x will always be 8.
The slope can be said to be "infinite", but since infinity is not a number, the slope in this case is "undefined", and that's what you should put down when taking a test.
The graph, once again, is just a vertical line extending in both directions forever, at x = 8.
Hope I helped!
The slope can be said to be "infinite", but since infinity is not a number, the slope in this case is "undefined", and that's what you should put down when taking a test.
The graph, once again, is just a vertical line extending in both directions forever, at x = 8.
Hope I helped!
I don't get this?
Help!
Help!
Well, It'd help if you told us *what* you don't get..
Just a suggestion.
 tempest
Just a suggestion.
 tempest
For the Slope, my teacher told me to take Y sub two minus y sub one, and the same for x. however, it looks like Sal did y sub one minus y sub two for one of the problems. can you do that or does it matter which way you do it?
Either way is fine. The only thing to be sure of is that you're consistent. If you did y₂y₁ and x₁x₂ you'd get the opposite of the slope, so make sure that one point either comes first or second both times.
How can we solve this type of problems?
How would you graph negative 5x + 6 if you wanted to?
Are you saying the variable is negative like "5x+6" or the whole expression is negative like "(5x+6)"? Because these are two completely different.
5x+6 has a slop of 5 (meaning that the line goes up 5 units in the ydirection while going left 1 unit in the xdirection) and the first point you would graph, starts at (0,6) which is 6 on the yaxis.
(5x+6) however means the whole expression is being multiplied by 1. Which then means you would get 5x 6. This would mean you would have the same slope as the previous (up 5 units in the ydirection and 1 unit to the left in the xdirection) but it also means the first point to graph would be 6 instead of +6.
This would result in two lines which have the exact same slope (and therefore parallel) but are 12 units apart in the ydirection (meaning one starts out at +6 on the yaxis and the other starts out at 6 on the yaxis.
Hope this helps!
5x+6 has a slop of 5 (meaning that the line goes up 5 units in the ydirection while going left 1 unit in the xdirection) and the first point you would graph, starts at (0,6) which is 6 on the yaxis.
(5x+6) however means the whole expression is being multiplied by 1. Which then means you would get 5x 6. This would mean you would have the same slope as the previous (up 5 units in the ydirection and 1 unit to the left in the xdirection) but it also means the first point to graph would be 6 instead of +6.
This would result in two lines which have the exact same slope (and therefore parallel) but are 12 units apart in the ydirection (meaning one starts out at +6 on the yaxis and the other starts out at 6 on the yaxis.
Hope this helps!
If you have the equation y = 5x + 6, then the slope is 5 and the yintercept is 6.
Because the yintercept is 6, the line passes through the point (0,6).
To get a second point that the line passes through, start with any point on the line (the yintercept will do) and add 1 to the xvalue and add the slope to the yvalue. So the second point will be (0+1, 6+(5)) which is (1,1).
So we mark the points (0,6) and (1,1) on the graph and draw a straight line through them, and that's our graph of y = 5x + 6.
Because the yintercept is 6, the line passes through the point (0,6).
To get a second point that the line passes through, start with any point on the line (the yintercept will do) and add 1 to the xvalue and add the slope to the yvalue. So the second point will be (0+1, 6+(5)) which is (1,1).
So we mark the points (0,6) and (1,1) on the graph and draw a straight line through them, and that's our graph of y = 5x + 6.
Does anyone know WHY this works?
And why is it always y=x+(number) or y=x(number). Why not just have say, 3 coordinates? So say x,y,s. (s for slope).
And why does y=y/x+(number). I get it in terms of algebra but why do we solve it the way we do?
And why is it always y=x+(number) or y=x(number). Why not just have say, 3 coordinates? So say x,y,s. (s for slope).
And why does y=y/x+(number). I get it in terms of algebra but why do we solve it the way we do?
If you have a 2dimensional coordinate plane, the y = ax + b is the form of the equation that will graph as a straight line. It's not a choice, that's just the way it is. Pick a and b. Let's say you pick 3 and 8. Now you have y = 3x + 8. That's an equation of a straight line. Try it and see. Put in a bunch of numbers for x. Calculate y for each one. Graph each of those points. You will see a straight line
I know that m is the slope.But what are exactly b and y
Y is the dependent variable. b is the yinterecept, which is the place where the line intersects the y axis. When x is 0, y = b.
How would you find the slope of the line for 4x  3y = 16?
Slope is 'm' in standard form: y=mx+b
So, you have to get that equation into standard form and then see what's in front of the x.
4x  3y = 16
+4x........+4x......(the 4x's cancel out on the left side)....(the dots are for spacing)
.......3y=4x+16
(divide both sides by 3)
y=4/3x16/3
Notice '4/3' is in front of the x, so it would be 'm' in y=mx+b, or the slope.
Slope= 4/3
:)
So, you have to get that equation into standard form and then see what's in front of the x.
4x  3y = 16
+4x........+4x......(the 4x's cancel out on the left side)....(the dots are for spacing)
.......3y=4x+16
(divide both sides by 3)
y=4/3x16/3
Notice '4/3' is in front of the x, so it would be 'm' in y=mx+b, or the slope.
Slope= 4/3
:)
In 9:30, I don't get how the slope of the line is 6. How did you get that?
i have heard that m=tan(theta)....is this right??
if it is right then please prove it to me.....thanx!
if it is right then please prove it to me.....thanx!
Yes, It is correct. Because m = rise/run.
and tan(theta) = opposite/ adjacent
Where theta = angle formed by the line on graph and "run".
Opposite = "rise"
adjacent = "run"
hence tan(theta) = opp/adj = rise/run = m
and tan(theta) = opposite/ adjacent
Where theta = angle formed by the line on graph and "run".
Opposite = "rise"
adjacent = "run"
hence tan(theta) = opp/adj = rise/run = m
what is F(x) mean, what is the function
I think F is basically whatever you need to do to X (you know, multiply it by the slope, add the intercept) to get Y. I'm not completely sure, though. Look it up
Shouldn't the formula for slope slope formula: m = [y1  y2] / [x1  x2]
The triangle represents the change in something. Δy means change in y, which is y1y2. Same thing for x, Δx means change in x.
At 8:00 you divide 6 by 3, for no reason. It doesn't make any sense to do that. 5/6 is not the same as 5/2, which means you ruined the equation. WHy would you divide the denominator only?
Hi I've been doing practice work on this but i don't understand what to do when the problem says like, "x=3" or like, "x+y=50"! How do I solve them?!?!!?!
For the 4th problem, The line contains (3,5) and (3,0), is y=5/6x+ 2.5 also an acceptable outcome?
For slope, all of the numbers will be fractions, not decimals.
I'm not sure if that is the question you are asking, I apologize if it is not.
Hope I answered your question!
I'm not sure if that is the question you are asking, I apologize if it is not.
Hope I answered your question!
At around 1:32, isn't the point that Sal's focusing on the Y intercept?
does the first number in the points (ie 0,1) matter at all?
Depending on which thing he shows in the video.
At 14:28, it mentions using function notation for the answer. Would it be counted wrong of you put "y"?
If you write y without saying what y is, then technically it's not right.
At 10:57, Sal defines y=f(x), so after that, it's cool to write y wherever you'd write f(x).
At 10:57, Sal defines y=f(x), so after that, it's cool to write y wherever you'd write f(x).
the slope is the same thing as gradient right?
what is the slope intercept form if the given is x=3?
The slop is undefined (some would say infinite), and there is no y intercept. So you can't write it in slopeintercept form.
if you are using an inch graph rather than a cm graph, will you still be able to determine the slope visually?
Yes, you will still be able to tell slope visually. You can count the squares up and over to find slope visually. Good question!
Yes, but if it is smaller it might be a little more difficult. The easiest case to visually find the slope is if it crosses a point where an x and y line meet.
What if it's a fraction
It doesn't but it makes it look more difficult though
Don't be intimidated by fractions. They are just numbers. It makes no difference.
Honestyly, this video is too long. I couldn't stay focused...
This is cool and all but why are we learning it? For graghs without formula's can someone elaborate upon that. (I understand I'm just wondering why I care)
cant you just count up the across
No, you need to do across then up. Up then across is a different equation. You can't do 4 up then 2 across, because that is different than 2 across than 4 up. :)
what is the little head that pops up and says "I don't understand that"?
For the problem "the line contains points (3,5) (3,0) he the 0 from the y coordinate first and got 5/6 but would if he use the 5 first would he have gotten 5\6 instead of 5\6? im confused because he said you can work the problem anyway and get the same answer
What is the function notation for y?
i need to write an equation of a line in slope intercept form that goes thorugh points (2,3) and is perpendicular to yaxis
Any line perpendicular to the yaxis will have a slope of 0. That gives us y=0x+b, which is the same as y=b. this means that the y value is always the same as the yintercept, so b=3. So your final equation is y=0x+3, or just y=3.
How to solve 4x+3y=22
Solving for y intercept 4x+3y=22
Solving y intercept
how do I find the slopeintercept form of an equation. for example: 3x2y=16. how do I do this?
We could not find where to submit our own questions.
Could someone help us?
Could someone help us?
I tried the practice and it gives me questions TOATALY unrelated to the video!
Is there any other videos that are there before the next level of the skill? If so, watch those before you try it. If not, then your computer is probably down, and confused webpages, so reload, or even restart it. Then it should work.
and also, i know i spelled totaly wrong... so yeah...
what is it called when there is not any slope
A point. All lines, by definition, must have a slope. It could be a horizontal line (which has a slope of 0) or a vertical line (which has an undefined slope), or somewhere in between. Since all lines can be described with a riseoverrun expression, all lines have slopes.
7:30, when you say when "Y" is zero, you mean when "X" is zero because you're going to the "Y" intercept not the "X" intercept
In the video 2:57 they talk about the change i don't think i have learned this can anyone help me
what if they gave us an improper fraction. like 3 9/10. do we have to make it into an mixed number?
You must make it 39/10
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