Question

What is the equation of the line passing through `(-5,4)` and `(9,-4)`?

Answer 1

`y=-4/7x+8/7`
or `4x+7y=8`

Explanation:

First up, it's a line, not a curve, so a linear equation. The easiest way to do this (in my view) is using the slope intercept formula which is `y=mx+c`, where `m` is the slope (the gradient) of the line, and c is the y-intercept.

The first step is the calculate the slope:
If the two points are `(x_1, y_1)" and "(x_2, y_2)`, then

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

`=>m=(-4-4)/(9-(-5))`

`=>m=(-4-4)/(9+5)`

`=>m=-8/14`

`=>m=-4/7`

So we now know a bit of the equation:

`y=-4/7x+c`

To find `c`, substitute in the values for `x` and `y` from any one of the two points, so using `(-5,4)`

`(4)=-4/7(-5)+c`

And solve for c

`=>4=(-4*-5)/7+c`

`=>4=20/7+c`

`=>4-20/7=c`

`=>(4*7)/7-20/7=c`

`=>28/7-20/7=c`

`=>8/7=c`

Then put in `c` and you get:

`y=-4/7x+8/7`

If you want, you can rearrange this into the general form:

`=>y=1/7(-4x+8)`

`=>7y=-4x+8`

`4x+7y=8`

And your graph would look like:
graph{4x+7y=8 [-18.58, 21.42, -9.56, 10.44]}

(you can click and drag on the line until you get the points if you want to double check)