Question

Find the equation of the line containing the given points. Write the equation in​ slope-intercept form, if possible. Graph the line? (-2,7); (1,-8)

find the equation

Answer 1

`y=-5x-3`

Explanation:

First off, slope-intercept form is `y=mx+b`
`x` and `y` are both coordinates for a given point such as (-2,7) and (1,-8)

`m` is the slope of the line which is "rise over run" or the change in `y` divided by the change in `x`.

So our first step is to get m by using our two coordinates by subtracting one `y` from the other and subtracting the coordinating `x` from the other `x`. This means that there is no necessary way to pick which `y` to subtract from which, but as long as you use one coordinate set to subtract the other, you'll be ok.

For our case we would have either
`(7- -8)/(-2-1)` or `(-8-7)/(1--2)`
the double negatives turn into pluses and the answers are
`15/-3` or `(-15)/3`
Either way, the answer is `-5` for `m`

so now that we know our `m` and we are given possible `x,y` pairs, we can solve for `b`.

We do this by inserting one of our coordinate sets into the equation
`(-2,7)` as `7=-5*-2 +b`
`(1,-8)` as `-8=-5*1 +b`

If we solve for `b` by multiplying `m` by `x` then subtracting that number from `y`, we should have `b`.

`7=-5*-2+b`
`7=10+b`
`-3=b`

`-8=-5*1+b`
`-3=b`

We can get `b` through either coordinate and it will be the same.

Lastly, we put all the information together to get:
`y=-5x-3` as our answer

The simple way to graph a line given by two coordinates is to graph out each one and drawing a line between the two. We really don't need the equation to do so, but it helps us double check our line (especially at `+b` which is where the line crosses the `x` axis.

If you need more help with this part, ask and I can add more.
graph{y=-5x-3 [-10, 10, -5, 5]}
should look like this though