Question

What is the slope-intercept form of the line passing through `(-6, 8)` and `(-3, 5)`?

Answer 1

`y=-x+2`

Explanation:

Alright, so this is a two-part question. First we need to find the slope, then we need to find the y-intercept. Finally we plug all this into the slope intercept equation `y=mx+b`

The slope is commonly referred to as `m=(rise)/(run)` this can also be expressed as `m=(y_2-y_1)/(x_2-x_1)` by using the change in `y` and the change in `x`.

`m=(5-8)/(-3-(-6))`

`m=(-3)/3`

`color(red)(m=-1)`

Alright, now lets find the y-intercept by using that slope. If we plug that slope into the base formula we get `y=-x+b`. Since we already know one point, lets put `(-3, 5)` into that equation and solve for `b`.

`5=-(-3)+b`

`5-3=3+b-3`

`color(red)(2=b)`

Now is if plug out `b` into out equation, we get a finally answer of `color(red)(y=-x+2)`

Even though we're done, lets check it by putting in the other point.

`8=-(-6)+2`

`8-6=6+2-6`

`color(red)(2=2)`

Hope this helps!
~Chandler Dowd