Question

a line passes through the points (-13, 8) and (7, -4). write its equation in slope-intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Calculate the slope

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-13,8)$ and $(x_2,y_2)=(7,-4)$.
$m = \frac{-4 - 8}{7 - (-13)} = \frac{-12}{20} = -\frac{3}{5}$

Step2: Find y-intercept $b$

Use slope-intercept form $y = mx + b$, substitute $m=-\frac{3}{5}$ and point $(-13,8)$.
$8 = -\frac{3}{5}(-13) + b$
$8 = \frac{39}{5} + b$
$b = 8 - \frac{39}{5} = \frac{40}{5} - \frac{39}{5} = \frac{1}{5}$

Step3: Write final equation

Substitute $m$ and $b$ into $y=mx+b$.
$y = -\frac{3}{5}x + \frac{1}{5}$

Answer:

$y = -\frac{3}{5}x + \frac{1}{5}$