Question

what is an equation of the line that passes through the points (-6, 8) and (3, -4)?

Explanation:

Step1: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
Let $(x_1,y_1)=(-6,8)$ and $(x_2,y_2)=(3,-4)$
$m=\frac{-4-8}{3-(-6)}=\frac{-12}{9}=-\frac{4}{3}$

Step2: Find y-intercept $b$

Use point-slope form $y-y_1=m(x-x_1)$, substitute $m=-\frac{4}{3}$ and $(x_1,y_1)=(-6,8)$
$y-8=-\frac{4}{3}(x-(-6))$
$y-8=-\frac{4}{3}(x+6)$
$y-8=-\frac{4}{3}x - 8$
$y=-\frac{4}{3}x$

Answer:

$y=-\frac{4}{3}x$ (or in standard form: $4x + 3y = 0$)