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Gestion de données, fonctions

## Multiple examples of constructing linear equations in slope-intercept form

Linear Equations in Slope Intercept Form
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## Multiple examples of constructing linear equations in slope-intercept form

Discussion and questions for this video
I don't understand why we divide by three at about 7:50. help?
1 Comment
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
how do you change from point-slope form to slope-intercept?
Comment
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

1 Comment
Why do we use X as the common variable in algebra? X is also the horizontal axis in graphs.
Comment
That's not a coincidence, as you will see when you start graphing algebraic equations.
1 Comment
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?
Comment
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.
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!
1 Comment
at 3:27 shoudnt it be y2-y1 over x2-x1 instead of y1-y2 over x1-x2
Comment
Believe it or not, they are the same thing. Try it.
Why is 6/-3 equal to -6/3 or -2?
Comment
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.
1 Comment
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?
Comment
The y-intercept can be any number, it need not be a whole number (usually is not). You just plot 2.5 as best you can, half-way between 2 and 3.
to find the slope sal subtracts (at 3:00) 6-0/2-5. check. next problem i paused, tried to figure it out myself and subtracted (at 5:54) 5-0/3-(-3) to find the slope. sal however reversed the order and did 0-5/-3-3. 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.
Comment
Ramona, it looks like you are on the right track. Continuing from your set up, you should get this result:
slope = (5-0)/(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."_
Comment
This isn't exactly related to the topic, but why does 6-0/2-5 become -6/-3 ?
Why isn't it just 6/-3 ? I never understood this and it always stuffs me up.
Comment
Tomm0,
Your mistake is that (6-0) 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 (6-0)/2-5)
(6-0) is +6 , not -6
(2-5) is -3
So the fraction is 6/-3
which reduces to -2/1 = -2

I hope that helps make it click for you.
1 Comment
How Would You Work This Type Of Problem When It's Set Up In A Table???
do you mean if its like
x-2/3/4/5/6
y-4/6/8/10/12 you have to find a pattern (in this case y is twice the amount of x) so y=2x
Comment
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?
Comment
I think I understand what you are trying to say, if you are talking about the equation y2-y1/x2-x1. So you would have 0-6/5-2. 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 6-0/2-5 or the way 0-6/5-2. You probably thought that 0-6 was just 6, but 0-6 is -6. Then you get 5-2 which is 3, so -6/3. If you thought 0-6 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
write th equation of the line in slope- intercept form if the slope is 1/5 and the y-intercept is -9
1 Vote
Comment
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
Comment
What if the slope is undefined, but you are given a point. What do you do?
Comment
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.
Comment
what do i do when the equation is Y = X
1 Vote
Comment
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.
Comment
AT 2:23 I don't get how he got -x
Comment
Try watching the video again.
Comment
How do I write the slope-intercept form of the equation of the line through: (3,-2), if the slope is undefined?
Comment
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 :-)
Comment
I didn't understand the equation f(1.5)=-3,f(-1)=2?
1 Vote
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
Comment
how do you find a y intercept in a graph
Comment
i don't understand what is going on when you have to solve for b, can i please have some help?
Comment
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.
1 Vote
Comment
how is it " m=delta y over delta x? " why is it not delta x over delta y?
1 Vote
Comment
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.
Comment
Is it m=y2-y1 over x2-x1 or m=y1-y2 over x1-x2? I need help. Please and Thank You.
1 Vote
Comment
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 y1-y2=-(y2-y1), annd the same for the x's, so multiply one way by -1/-1, and you'll get the other.
Comment
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?
Comment
@ 1:07} Do you have to use m to represent the slope or do you choose any variable?
Comment
Well technically, you have to use m to represent the slope or else it wouldn't be right.
1 Vote
Comment
How do you make it easier to convert from a problem such as -5x + 2y = 6 without getting confused over negative numbers?
1 Vote
Comment
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!
Comment
at 3:53 , why does Sal put a negative when 6 - 0 is not negative?
1 Vote
Comment
because he went the other way around just to prove you would get the same value for the slope.
1 Comment
how do i find an equation of the slope line?
Comment
I do not get your question.
it is y1 -y2 over x1- x2
1 Vote
Comment
How do you solve a problem when it asks you, " Write the equation that describes each line in slope-intercept 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!!!!!!!
Comment
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.
1 Vote
Comment
And when graphing these can if you can switch the 6/-3 around will it change the graph points
Comment
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 X2-X1.
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: 4-2 over 3-1 which is 2 over 2 which can be simplified to 1. The slope of the equation is 1.
Hope this helped!
1 Vote
Comment
Isn't -2-1=3 ? Sal said that it equals to 2?!
1 Vote
Comment
The answer is not 2. Probably just a simple mistake
1 Comment
if you have 2lbs of jellybeans for $9, what of .5 lbs? 3lbs? 4 lbs? 2 Votes Comment 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 1 Vote Comment 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 2 Votes Comment what is the *slope-intercept formula* 1 Vote Comment and x and y are points on the graph. 2 Votes Comment at 1:48 how did he find the y-intercept of the equation if it was not written in standard form ? 2 Votes 1 Comment 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. 1 Vote Comment 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?
Comment
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.
1 Vote
Comment
Will you please show how to find the slope-intercept form for the line satisfying the following:
x-intercept 3, y-intercept 2/3?
Comment
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!
1 Vote
Comment
How do you write the the equation if its a word problem?
Comment
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.
1 Vote
Comment
what is the x for ?
1 Vote
Comment
Its the value of the number on the x axis.

Oh yeah, - x is just a variable.
Comment
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)
Comment
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.
1 Vote
Comment
Is there a particular reason why Sal used less common variables in this video? Or did he just want to through in a variety?
1 Vote
Comment
Well, if you are talking about him using the variables: m, x, y, and b, he is using the equation of slope-intercept form, which is *y = xm + b*. "b" is the y-intercept 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/linear-equations-and-inequalitie/equation-of-a-line/v/graphing-a-line-in-slope-intercept-form.

Also, the f at around 10:32 is a symbol for function.
1 Vote
Comment
at 2:57 in the videos sal used these triangular shaped things in the equation what are they and what do they represent
1 Vote
Comment
They are the Greek symbol delta. They are accepted in math and science as the word "change".
1 Comment
How do you write an equation in slope intercept form?
1 Vote
Comment
A linear equation in slope-intercept form is y = mx + b. Where "m" is your slope and "b" is your y-intercept.
Comment
How to graph y=x
Comment
The y-intercept would be zero and the slope would be 1.It would have a constant increase and go in a straight equal line.
1 Vote
Hi you have done that in a problem
Line contain points (2,6) and (5,0)
m=y1-y2/x1-x2

but the formula is
http://cs.selu.edu/~rbyrd/math/slope/slo_eq1.gif
1 Vote
Comment
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.
Comment
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, "6-0/2-5"

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 "0-5/3 - -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,

"5-0/ -3-3"

Sal's Equation: "0-5/ 3- -3"
1 Vote
Comment
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!
Comment
what does delta mean?
1 Vote
Comment
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.
Comment
what is linear equation
1 Vote
Comment
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.
Comment
How are you supposed to find the fraction
aka the answer?! I need help.. any1?
Comment
IM THE SHORT GUY PEOPLE PLZ HELP!.... and thx and i wonder who else needs help ..
1 Vote
Comment
1 Vote
Comment
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.
x-x+2y=5-x so
2y=5-x 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 y-intercept form. The slope is -1/2 and the y-intercept is the point (0,5/2)
At 7:20 why did he choose the second point, what if the first piont??
1 Vote
Comment
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
Comment
how do i make 6x - 3y = -9 in slope intercept form
1 Vote
Comment
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/
Comment
how do i solve 6x - 3y = -9 for y
1 Vote
Comment
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
Comment
i dont understand why negatives cancel out
1 Vote
Comment
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.
Comment
Why does he subtract the two points when one is greater in x and y values than the other?
1 Vote
Comment
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=(y2-y1)/(x2-x1). 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.
i cant figure out what (34,87) (51,25) can u plaese help me
Comment
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?
1 Vote
Comment
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.

I thought it was y2 - y1 over x2 - x1.
1 Vote
Comment
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!
Comment
At 3:28 why does he put the first coordinate first? the equation is y>2- y>1
x>2- x>1
Comment
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.
1 Vote
1 Comment
how would you determinr the the rate of change is constant for tables given.
1 Vote
Comment
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 (7-5)/4-3) = 2/1 = 2
The second & third term (11-7)/(6-4) = 4/2 = 2
So far the change is constant
The third and fourth term (14-11)/(7-6) = 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.
Comment
what does f(x) - f of x mean?
1 Vote
Comment
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.
Comment
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?
1 Vote
Comment
Points that dont' satisfy the equation cannot be on the line.
Comment
Sorry, could someone explain to me why you multiply x by the slope?
Comment
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
Comment
When finding the slope from the points could you just stack and subtract? Would that work everytime for points?
1 Vote
Comment
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.
Comment
what if all you have are two points? how would you find the y-intercept? I still don't understand!!
1 Vote
Comment
Two points define a line, and if you define a line, then you define the y-intercept. 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.
Comment
Please explain how to graph the equation and state the slope of the line if the slope existed Example x=-8
1 Vote
Comment
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!
Comment
I don't get this?
Help!
1 Vote
Comment
Well, It'd help if you told us *what* you don't get..
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?
Comment
Either way is fine. The only thing to be sure of is that you're consistent. If you did y₂-y₁ and x₁-x₂ you'd get the opposite of the slope, so make sure that one point either comes first or second both times.
Comment
How would you graph negative 5x + 6 if you wanted to?
1 Vote
Comment
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 y-direction while going left 1 unit in the x-direction) and the first point you would graph, starts at (0,6) which is 6 on the y-axis.

-(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 y-direction and 1 unit to the left in the x-direction) 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 y-direction (meaning one starts out at +6 on the y-axis and the other starts out at -6 on the y-axis.

Hope this helps!
Comment
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?
1 Vote
Comment
If you have a 2-dimensional 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
Comment
I know that m is the slope.But what are exactly b and y
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Y is the dependent variable. b is the y-interecept, which is the place where the line intersects the y axis. When x is 0, y = b.
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How would you find the slope of the line for -4x - 3y = 16?
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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=-4/3x-16/3

Notice '-4/3' is in front of the x, so it would be 'm' in y=mx+b, or the slope.
Slope= -4/3
:)
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In 9:30, I don't get how the slope of the line is -6. How did you get that?
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i have heard that m=tan(theta)....is this right??
if it is right then please prove it to me.....thanx!
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Yes, It is correct. Because m = rise/run.
Where theta = angle formed by the line on graph and "run".
Opposite = "rise"
hence tan(theta) = opp/adj = rise/run = m
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what is F(x) mean, what is the function
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k thanks
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Shouldn't the formula for slope slope formula: m = [y1 - y2] / [x1 - x2]
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The triangle represents the change in something. Δy means change in y, which is y1-y2. Same thing for x, Δx means change in x.
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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?
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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?!?!!?!
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For the 4th problem, The line contains (3,5) and (-3,0), is y=5/6x+ 2.5 also an acceptable outcome?
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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.
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At around 1:32, isn't the point that Sal's focusing on the Y intercept?
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does the first number in the points (ie 0,1) matter at all?
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Depending on which thing he shows in the video.
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At 14:28, it mentions using function notation for the answer. Would it be counted wrong of you put "y"?
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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).
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the slope is the same thing as gradient right?
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what is the slope intercept form if the given is x=3?
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The slop is undefined (some would say infinite), and there is no y intercept. So you can't write it in slope-intercept form.
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if you are using an inch graph rather than a cm graph, will you still be able to determine the slope visually?
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Yes, you will still be able to tell slope visually. You can count the squares up and over to find slope visually. Good question!
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What if it's a fraction
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It doesn't but it makes it look more difficult though
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Honestyly, this video is too long. I couldn't stay focused...
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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)
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cant you just count up the across
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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. :)
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what is the little head that pops up and says "I don't understand that"?
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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
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What is the function notation for y?
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i need to write an equation of a line in slope intercept form that goes thorugh points (2,3) and is perpendicular to y-axis
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Any line perpendicular to the y-axis 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 y-intercept, so b=3. So your final equation is y=0x+3, or just y=3.
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How to solve 4x+3y=22
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3y=--4x+22
y=--4/3+22
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Solving for y intercept 4x+3y=22
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Solving y intercept
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how do I find the slope-intercept form of an equation. for example: 3x-2y=-16. how do I do this?
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We could not find where to submit our own questions.
Could someone help us?
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I tried the practice and it gives me questions TOATALY unrelated to the video!
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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.
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what is it called when there is not any slope
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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 rise-over-run expression, all lines have slopes.
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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
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In the video 2:57 they talk about the change i don't think i have learned this can anyone help me
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what if they gave us an improper fraction. like 3 9/10. do we have to make it into an mixed number?
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You must make it 39/10
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