Question

what is an equation of the line that passes through the points $(-2, 4)$ and $(3, -6)$?

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-2,4)$ and $(x_2,y_2)=(3,-6)$:
$m=\frac{-6-4}{3-(-2)}=\frac{-10}{5}=-2$

Step2: Use point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(-2,4)$ and $m=-2$:
$y-4=-2(x-(-2))$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y-4=-2(x+2)$
$y-4=-2x-4$
$y=-2x$

Answer:

$y=-2x$