Question

a line passes through the points (-3, 2) and (5, -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 $(x_1,y_1)=(-3,2)$ and $(x_2,y_2)=(5,-4)$.
$m=\frac{-4-2}{5-(-3)}=\frac{-6}{8}=-\frac{3}{4}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=-\frac{3}{4}$ and point $(-3,2)$.
$2 = -\frac{3}{4}(-3) + b$
$2 = \frac{9}{4} + b$
$b = 2 - \frac{9}{4} = \frac{8}{4} - \frac{9}{4} = -\frac{1}{4}$

Step3: Write final equation

Combine slope and y-intercept in $y=mx+b$.
$y = -\frac{3}{4}x - \frac{1}{4}$

Answer:

$y = -\frac{3}{4}x - \frac{1}{4}$