Question

find an equation for the line that passes through the points (3, -6) and (-3, -3).

Explanation:

Step1: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Let $(x_1,y_1)=(3,-6)$ and $(x_2,y_2)=(-3,-3)$
$m=\frac{-3-(-6)}{-3-3}=\frac{3}{-6}=-\frac{1}{2}$

Step2: Find y-intercept $b$

Use point-slope form $y-y_1=m(x-x_1)$, substitute $(3,-6)$ and $m=-\frac{1}{2}$:
$y-(-6)=-\frac{1}{2}(x-3)$
Simplify to slope-intercept form $y=mx+b$:
$y+6=-\frac{1}{2}x+\frac{3}{2}$
$y=-\frac{1}{2}x+\frac{3}{2}-6$
$y=-\frac{1}{2}x-\frac{9}{2}$

Answer:

$y=-\frac{1}{2}x-\frac{9}{2}$
(or in standard form: $x+2y=-9$)