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## Algebra 1

### Course: Algebra 1 > Unit 5

Lesson 3: Writing slope-intercept equations- Slope-intercept equation from graph
- Writing slope-intercept equations
- Slope-intercept equation from graph
- Slope-intercept equation from slope & point
- Slope-intercept equation from two points
- Slope-intercept from two points
- Constructing linear equations from context
- Writing linear equations word problems
- Slope-intercept form review

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# 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(198 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.(57 votes)

- i think i'll just sell corn on the street(63 votes)
- fr but i think lemonade would be better(23 votes)

- everything about what we are learning I don't understand(56 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.(29 votes)

- What is the rule with deciding which point value gets subtracted from the other?(21 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)(20 votes)

- Bruh this is hard to do. I still dont undertand(29 votes)
- no way that this makes a single drop of sense(26 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.(2 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.

(12 votes)

- my head hurts(17 votes)
- fr like im just gonna be physical therapist so i dont have to do math(6 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`

(18 votes)

- bro why does hurt my brain

like i did fine on my Quiz(14 votes)