Question

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find an equation for the line below.

Explanation:

Step1: Identify two points

The line passes through $(-1, 2)$ and $(-5, -4)$.

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-4-2}{-5-(-1)}=\frac{-6}{-4}=\frac{3}{2}$

Step3: Use point-slope form

Use point $(-1,2)$: $y-y_1=m(x-x_1)$
$y-2=\frac{3}{2}(x-(-1))$

Step4: Simplify to slope-intercept

$y-2=\frac{3}{2}x+\frac{3}{2}$
$y=\frac{3}{2}x+\frac{3}{2}+2$
$y=\frac{3}{2}x+\frac{7}{2}$

Answer:

$y=\frac{3}{2}x+\frac{7}{2}$