I think I may need to give up and be a farmer because this is to hard

Alexis, I am in my 40's relearning this. Don't give up. Plus, farmers use TONs (TONNES, depending on where you live) of maths. Keep practicing, every wrong answer is still learning.

i think i'll just sell corn on the street

fr but i think lemonade would be better

everything about what we are learning I don't understand

You may need to go back to wherever you feel comfortable with, and learn upward again slowly. You can do this within Khan Academy.

no way that this makes a single drop of sense

The first step (Finding the slope) isn't all that difficult. You just need to subtract while remembering which numbers go where. But when finding the y intercept.. I'm completely lost lol.

Bruh this is hard to do. I still dont undertand

If you need help, just watch the videos or look up the answers on Google. If you don't understand the videos, Khan Academy will try their best to improve their videos and their website.

fr like im just gonna be physical therapist so i dont have to do math

What is the rule with deciding which point value gets subtracted from the other?

It doesn't matter. The only difference is that there's a sign change, but since this happens both for 𝛥𝑦 as for 𝛥𝑥 these changes cancel out when we divide the two (𝛥𝑦∕𝛥𝑥). 𝛥𝑦 = 𝑦₂ − 𝑦₁ = −(𝑦₁ − 𝑦₂) 𝛥𝑥 = 𝑥₂ − 𝑥₁ = −(𝑥₁ − 𝑥₂) ⇒ 𝛥𝑦∕𝛥𝑥 = (𝑦₂ − 𝑦₁)∕(𝑥₂ − 𝑥₁) = −(𝑦₁ − 𝑦₂)∕(−(𝑥₁ − 𝑥₂)) = (𝑦₁ − 𝑦₂)∕(𝑥₁ − 𝑥₂)

On number 4, why would b=17?

This is the process they show you: y =−4x+b 9 =−4⋅2+b 9 =−8+b 17=b ---------- In THIS ("9 =−8+b") step they are subtracting -8 from 9 which looks like this: 9-(-8). We know that two negative operations make a positive sum, which is why the answer is 17 : 9-(-8) = 17.

how do you change 7x+3y=3 into slope intercept form

For something to be in slope-intercept for, y needs to be isolated on one side of the equation. Here's how you'd do that: ```7x + 3y = 3``` Subtract 7x from both sides: ```7x + 3y - 7x = 3 - 7x``` Simplify: ```3y = 3 - 7x``` Now, divide both sides by 3: ```3y/3 = 3/3 - 7x/3``` Simplify: ```y = 1 - (7/3)x``` Usually, we have the intercept (in this case 1) on the right side, so simply move it: ```y = -(7/3)x + 1```

Main content

Course: Grade 8 (Virginia) > Unit 4

Lesson 3: Writing slope-intercept equations

Writing slope-intercept equations

Google Classroom

Learn how to find the slope-intercept equation of a line from two points on that line.

If you haven't read it yet, you might want to start with our introduction to slope-intercept form.

Writing equations from $y$ ‍-intercept and another point

Let's write the equation of the line that passes through the points

(0, 3)

and

(2, 7)

in slope-intercept form.

Recall that in the general slope-intercept equation

y = m x + b

, the slope is given by

m

and the

y

-intercept is given by

b

Finding $b$ ‍

The

y

-intercept of the line is

(0, 3)

, so we know that

b = 3

Finding $m$ ‍

Recall that the slope of a line is the ratio of the change in

y

over the change in

x

between any two points on the line:

Slope = \frac{Change in y}{Change in x}

Therefore, this is the slope between the points

(0, 3)

and

(2, 7)

\begin{aligned} m & = \frac{Change in y}{Change in x} \\ = \frac{7 - 3}{2 - 0} \\ = \frac{4}{2} \\ = 2 \end{aligned}

In conclusion, the equation of the line is $y = 2 x + 3$ ‍.

Check your understanding

Problem 1

Write the equation of the line.

Problem 2

Write the equation of the line.

Writing equations from any two points

Let's write the equation of the line that passes through

(2, 5)

and

(4, 9)

in slope-intercept form.

Note that we are not given the

y

-intercept of the line. This makes things a little bit more difficult, but we are not afraid of a challenge!

Finding $m$ ‍

\begin{aligned} m & = \frac{Change in y}{Change in x} \\ = \frac{9 - 5}{4 - 2} \\ = \frac{4}{2} \\ = 2 \end{aligned}

Finding $b$ ‍

We know that the line is of the form

y = 2 x + b

, but we still need to find

b

. To do that, we substitute the point

(2, 5)

into the equation.

Because any point on a line must satisfy that line’s equation, we get an equation that we can solve to find

b

Substituting

(2, 5)

into the equation is the same as substituting

x = 2

and

y = 5

into the equation.

Remember that every point on the graph of a two-variable equation is a solution of that equation. In other words, if we substitute the point into the equation we get a true statement.

To use a different equation as an example, the point

(3, 1)

is on the line

y = x - 2

. This means that substituting the point into the equation will result in a true statement:

\begin{aligned} y & = x - 2 \\ 1 & = 3 - 2 & x = 3 and y = 1 \\ 1 & = 1 \end{aligned}

In our solution, we do the same thing, only we don't know the complete equation of the line. Substituting a point that we know is on the line will help us find the missing

b

\begin{aligned} y & = 2 \cdot x + b \\ 5 & = 2 \cdot 2 + b & x = 2 and y = 5 \\ 5 & = 4 + b \\ 1 & = b \end{aligned}

In conclusion, the equation of the line is $y = 2 x + 1$ ‍.

Check your understanding

Problem 3

Write the equation of the line.

Problem 4

Write the equation of the line.

Challenge problem

A line passes through the points

(5, 35)

and

(9, 55)

Write the equation of the line.

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Alexis
Posted 4 years ago. Direct link to Alexis's post “I think I may need to giv...”
I think I may need to give up and be a farmer because this is to hard
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- pdinthekr
  Posted 3 years ago. Direct link to pdinthekr's post “Alexis, I am in my 40's r...”
  Alexis, I am in my 40's relearning this. Don't give up. Plus, farmers use TONs (TONNES, depending on where you live) of maths. Keep practicing, every wrong answer is still learning.
  Comment on pdinthekr's post “Alexis, I am in my 40's r...”
  (131 votes)
ahernandez26
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i think i'll just sell corn on the street
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- patelaa
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  fr but i think lemonade would be better
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everything about what we are learning I don't understand
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- Thien D Ho
  Posted 6 years ago. Direct link to Thien D Ho's post “You may need to go back t...”
  You may need to go back to wherever you feel comfortable with, and learn upward again slowly. You can do this within Khan Academy.
  Comment on Thien D Ho's post “You may need to go back t...”
  (38 votes)
crosshillary
Posted 6 years ago. Direct link to crosshillary's post “What is the rule with dec...”
What is the rule with deciding which point value gets subtracted from the other?
Button navigates to signup pageButton navigates to signup page
(22 votes)
Answer
- Jerry Nilsson
  Posted 6 years ago. Direct link to Jerry Nilsson's post “It doesn't matter. The on...”
  It doesn't matter. The only difference is that there's a sign change, but since this happens both for 𝛥𝑦 as for 𝛥𝑥 these changes cancel out when we divide the two (𝛥𝑦∕𝛥𝑥).
  
  𝛥𝑦 = 𝑦₂ − 𝑦₁ = −(𝑦₁ − 𝑦₂)
  𝛥𝑥 = 𝑥₂ − 𝑥₁ = −(𝑥₁ − 𝑥₂)
  ⇒
  𝛥𝑦∕𝛥𝑥 = (𝑦₂ − 𝑦₁)∕(𝑥₂ − 𝑥₁) = −(𝑦₁ − 𝑦₂)∕(−(𝑥₁ − 𝑥₂)) = (𝑦₁ − 𝑦₂)∕(𝑥₁ − 𝑥₂)
  Comment on Jerry Nilsson's post “It doesn't matter. The on...”
  (24 votes)
ಥ_ಥ NickT
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no way that this makes a single drop of sense
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(32 votes)
Answer
- :|
  Posted a year ago. Direct link to :|'s post “The first step (Finding t...”
  The first step (Finding the slope) isn't all that difficult. You just need to subtract while remembering which numbers go where.
  But when finding the y intercept.. I'm completely lost lol.
  Comment on :|'s post “The first step (Finding t...”
  (7 votes)
KAITLYNL
Posted 4 years ago. Direct link to KAITLYNL's post “Bruh this is hard to do. ...”
Bruh this is hard to do. I still dont undertand
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- Han Maslowski
  Posted 3 months ago. Direct link to Han Maslowski's post “If you need help, just wa...”
  If you need help, just watch the videos or look up the answers on Google. If you don't understand the videos, Khan Academy will try their best to improve their videos and their website.
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my head hurts
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- Kyle
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  fr like im just gonna be physical therapist so i dont have to do math
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Anna
Posted 7 years ago. Direct link to Anna's post “On number 4, why would b=...”
On number 4, why would b=17?
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(20 votes)
Answer
- Diya
  Posted 6 years ago. Direct link to Diya's post “This is the process they ...”
  This is the process they show you:
  y =−4x+b
  9 =−4⋅2+b
  9 =−8+b
  17=b
  ----------
  In THIS ("9 =−8+b") step they are subtracting -8 from 9 which looks like this: 9-(-8). We know that two negative operations make a positive sum, which is why the answer is 17 : 9-(-8) = 17.
  
  Comment on Diya's post “This is the process they ...”
  (14 votes)
lylah amaya
Posted 4 years ago. Direct link to lylah amaya's post “bro why does hurt my brai...”
bro why does hurt my brain
like i did fine on my Quiz
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tmukono1
Posted 6 years ago. Direct link to tmukono1's post “how do you change 7x+3y=3...”
how do you change 7x+3y=3 into slope intercept form
Button navigates to signup pageComment on tmukono1's post “how do you change 7x+3y=3...”
(6 votes)
Answer
- Admiral Betasin
  Posted 6 years ago. Direct link to Admiral Betasin's post “For something to be in sl...”
  For something to be in slope-intercept for, y needs to be isolated on one side of the equation.
  Here's how you'd do that:
  7x + 3y = 3
  
  Subtract 7x from both sides:
  7x + 3y - 7x = 3 - 7x
  
  Simplify:
  3y = 3 - 7x
  
  Now, divide both sides by 3:
  3y/3 = 3/3 - 7x/3
  
  Simplify:
  y = 1 - (7/3)x
  
  Usually, we have the intercept (in this case 1) on the right side, so simply move it:
  y = -(7/3)x + 1
  Comment on Admiral Betasin's post “For something to be in sl...”
  (19 votes)

Grade 8 (Virginia)

Course: Grade 8 (Virginia) > Unit 4

Writing equations from y‍ -intercept and another point

Finding b‍

Finding m‍

Check your understanding

Writing equations from any two points

Finding m‍

Finding b‍

Check your understanding

Want to join the conversation?

Writing equations from $y$ ‍-intercept and another point

Finding $b$ ‍

Finding $m$ ‍

Finding $m$ ‍

Finding $b$ ‍