Answer
Point-slope form: $ y-2=-6(x+3)$.
Slope-intercept form: $y=-6x-16$.
Work Step by Step
If the line passes through a point $(x_1,y_1)$ and the slope is $m$, then the point-slope form of the line's equation is.
$\Rightarrow y-y_1=m(x-x_1)$.....(1)
We are given
$\Rightarrow (x_1,y_1)=(-3,2)$
$\Rightarrow m=-6$
Substitute all values into the equation (1).
$\Rightarrow y-(2)=(-6)(x-(-3))$
Simplify.
$\Rightarrow y-2=-6(x+3)$
The above equation is the point-slope form.
Now we will write the equation in the slope-intercept form
$y=mx+b$.
Isolate $y$.
Use the distributive property:
$\Rightarrow y-2=-6x-18$
Add $2$ to both sides.
$\Rightarrow y-2+2=-6x-18+2$
Simplify.
$\Rightarrow y=-6x-16$.
The above equation is the slope-intercept form.
