Question

find an equation for the line below.

Explanation:

Step1: Identify two points

The line passes through $(-3, -1)$ and $(5, -4)$.

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-4 - (-1)}{5 - (-3)}=\frac{-3}{8}$

Step3: Use point-slope form

Use point $(-3, -1)$: $y - y_1 = m(x - x_1)$
$y - (-1)=-\frac{3}{8}(x - (-3))$

Step4: Simplify to slope-intercept

$y + 1=-\frac{3}{8}x-\frac{9}{8}$
$y=-\frac{3}{8}x-\frac{9}{8}-1$
$y=-\frac{3}{8}x-\frac{17}{8}$

Answer:

$y=-\frac{3}{8}x-\frac{17}{8}$