Question

find an equation for the line below.

Explanation:

Step1: Identify two points

The line passes through $(-4, 4)$ and $(1, -4)$.

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-4-4}{1-(-4)}=\frac{-8}{5}$

Step3: Use point-slope form

Use point $(1, -4)$: $y-y_1=m(x-x_1)$
$y-(-4)=-\frac{8}{5}(x-1)$

Step4: Simplify to slope-intercept form

Expand and isolate $y$:
$y+4=-\frac{8}{5}x+\frac{8}{5}$
$y=-\frac{8}{5}x+\frac{8}{5}-4$
$y=-\frac{8}{5}x+\frac{8}{5}-\frac{20}{5}$
$y=-\frac{8}{5}x-\frac{12}{5}$

Answer:

$y=-\frac{8}{5}x-\frac{12}{5}$