Answer
Point slope form $y-5=-2(x+2)$ or $y-13=-2(x+6)$.
Slope-intercept form $y=-2x+1$.
Work Step by Step
The given points are
$(-2,5)$ and $(-6,13)$
Change in the $y-$coordinates $=13-(5)=8$.
Change in the $x-$coordinates $=-6-(-2)=-4$.
Slope of the line $m=\frac{change \; in \; y}{change \; in \; x}$.
$\Rightarrow m=\frac{8}{-4}$
$\Rightarrow m=-2$
The point slope form of the equation is
$\Rightarrow y-y_1=m(x-x_1)$
Plug $(x_1,y_1)=(-2,5)$ and slope $m$ into the above equation.
$\Rightarrow y-5=(-2)(x-(-2))$
Simplify.
$\Rightarrow y-5=-2(x+2)$
Plug $(x_1,y_1)=(-6,13)$ and slope $m$ into the above equation.
$\Rightarrow y-13=(-2)(x-(-6))$
Simplify.
$\Rightarrow y-13=-2(x+6)$
Now solve the above equation for $y$.
$\Rightarrow y-13=-2(x+6)$
Apply distributive property.
$\Rightarrow y-13=-2x-12$
Add $13$ to both sides.
$\Rightarrow y-13+13=-2x-12+13$
Add like terms.
$\Rightarrow y=-2x+1$
The above equation is the slope-intercept form.
