Question

find an equation for the line that passes through the points (-5, -4) and (3, -2).

Explanation:

Step1: Calculate the slope

The slope formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(-5,-4)$ and $(3,-2)$:
$m=\frac{-2-(-4)}{3-(-5)}=\frac{2}{8}=\frac{1}{4}$

Step2: Use point-slope form

Point-slope form: $y-y_1=m(x-x_1)$. Use $(3,-2)$:
$y-(-2)=\frac{1}{4}(x-3)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y+2=\frac{1}{4}x-\frac{3}{4}$
$y=\frac{1}{4}x-\frac{3}{4}-2$
$y=\frac{1}{4}x-\frac{3}{4}-\frac{8}{4}$
$y=\frac{1}{4}x-\frac{11}{4}$

Answer:

$y=\frac{1}{4}x-\frac{11}{4}$ (or in standard form: $x-4y=11$)