Question

What is the equation of the line between `(-7,2)` and `(7,-38)`?

Answer 1

Slope-intercept form: `y=-20/7 x-18`
Standard form: `20x+7y=-126`

Explanation:

I will assume that you want the equation in slope-intercept form. Here, we can use the format for finding the slope given two points, which is

`(y_2-y_1)/(x_2-x_1)`

In our problem `(x_1,y_1)` is `(-7,2)` and `(x_2,y_2)` `(7,-38)`. We can insert values and find the slope:

`(-38-2)/(7-(-7))=-40/(7+7)=-40/14=-20/7`

Next, we choose one of our coordinates and put that into the formula for a line in slope-intercept form,

`y=mx+b`

Let's choose `(-7,2)`:

`2=-20/7(-7)+b`
`2=20+b`
`-18=b`

This gives us our final equation, `y=-20/7 x-18`.

If you needed standard form, here's how we can do that:

`20/7 x+y=-18`
`7*(20/7 x+y)=(-18)*7`
`20x+7y=-126`

Hope this helps!