Question

a line passes through the points (-5, 9) and (15, -3). 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 for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(-5,9)$ and $(15,-3)$:
$m=\frac{-3-9}{15-(-5)}=\frac{-12}{20}=-\frac{3}{5}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=-\frac{3}{5}$ and point $(-5,9)$:
$9=-\frac{3}{5}(-5)+b$
$9=3+b$
$b=9-3=6$

Step3: Write final equation

Combine slope and y-intercept in $y=mx+b$:
$y=-\frac{3}{5}x+6$

Answer:

$y=-\frac{3}{5}x+6$