Question

What is the equation in point-slope form and slope intercept form for the line given (-3,6) and (2,-9)?

Answer 1

The point-slope form is `y-6=3(x+3)`, and the slope-intercept form is `y=3x+15` .

Determine the slope, `m`.

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

Let `(-3,6)=x_1,y_1` and `(2,-9)=x_2,y_2` .

`m=(-9-6)/(2-(-3))=15/5=3`

Point-slope Form

The general formula is `y-y_1=m(x-x_1)`

Use one of the points given as `x_1` and `y_1`. I'm going to use point `(-3,6)` which is consistent with finding the slope.

`x_1=-3`
`y_1=6`
`m=3`.

`y-6=3(x-(-3))` =

`y-6=3(x+3)`

Slope-intercept Form

The general formula is `y=mx+b`, where `m` is slope and `b` is the y-intercept.

Solve the point-slope form equation for `y`.

`y-6=3(x+3)`=

Add `6` to both sides.

`y=3(x+3)+6` =

Distribute the `3`.

`y=3x+9+6` =

`y=3x+15`

The slope is `3` and the `y`-intercept is `15`.