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### Course: Get ready for AP® Calculus > Unit 2

Lesson 2: Writing slope-intercept equations# Writing slope-intercept equations

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:

Therefore, this is the slope between the points $(0,3)$ and $(2,7)$ :

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

## Check your understanding

## 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 ${m}$

### 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 ${b}$ .

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

## Check your understanding

## Want to join the conversation?

- I think I may need to give up and be a farmer because this is to hard(253 votes)
- 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.(136 votes)

- i think i'll just sell corn on the street(85 votes)
- fr but i think lemonade would be better(43 votes)

- everything about what we are learning I don't understand(58 votes)
- You may need to go back to wherever you feel comfortable with, and learn upward again slowly. You can do this within Khan Academy.(38 votes)

- no way that this makes a single drop of sense(33 votes)
- 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.(7 votes)

- What is the rule with deciding which point value gets subtracted from the other?(22 votes)
- 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)(24 votes)

- Bruh this is hard to do. I still dont undertand(32 votes)
- 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.(3 votes)

- my head hurts(24 votes)
- fr like im just gonna be physical therapist so i dont have to do math(11 votes)

- On number 4, why would b=17?(20 votes)
- 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.

(14 votes)

- bro why does hurt my brain

like i did fine on my Quiz(16 votes) - how do you change 7x+3y=3 into slope intercept form(6 votes)
- 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`

(19 votes)