Question

what is an equation of the line that passes through the points $(-6, 6)$ and $(-3, 1)$?

Explanation:

Step1: Calculate slope $m$

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-6,6)$ and $(x_2,y_2)=(-3,1)$:
$m=\frac{1-6}{-3-(-6)}=\frac{-5}{3}$

Step2: Use point-slope form

Point-slope form: $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(-6,6)$:
$y-6=-\frac{5}{3}(x-(-6))$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y-6=-\frac{5}{3}(x+6)$
$y-6=-\frac{5}{3}x - 10$
$y=-\frac{5}{3}x - 10 + 6$
$y=-\frac{5}{3}x - 4$

Answer:

$y=-\frac{5}{3}x - 4$ (or in standard form: $5x + 3y = -12$)