Question

What is the equation of the line that passes through the points `(-1,3)` and `(3, -5)`?

Answer 1

`y+2x-1=0`

Explanation:

Let's say `A` is the point `(-1,3)` and `B` is the point `(3,-5)`

The equation of a line that passes through two points is `y-y_0=m(x-x_0)`

Replace `x, x_0, y` and `y_0` by the coordinates of the two points to find your slope`=>m`.

It doesn't matter which point you choose to replace `x, x_0, y` and `y_0` with as long as you pair `x` with `y` and `x_0` with `y_0`.

`m=(y-y_0)/(x-x_0)=(-5-3)/(3-(-1))=(-5-3)/(3+1)=-2`

Now, all you have to do is to choose either the coordinates of `A` or `B` to replace in the equation of a line that passes through two points `=>y-y_0=m(x-x_0)`. You are only going to replace `x_0` and `y_0`.

I'm using the point `A` `(-1,3)`

`=>y-y_0=m(x-x_0)`

`=>y-3=-2(x+1)`

`=>y-3=-2x-2`

`=>y+2x-1=0` is your line.

Try to use the other point and you'll see that you'll find the same line.

Hope this helps :)