Question

a line passes through the points (-2, -4) and (4, 6). 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 $(-2,-4)$ and $(4,6)$:
$m=\frac{6-(-4)}{4-(-2)}=\frac{10}{6}=\frac{5}{3}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=\frac{5}{3}$ and point $(4,6)$:
$6=\frac{5}{3}(4)+b$
$6=\frac{20}{3}+b$
$b=6-\frac{20}{3}=\frac{18}{3}-\frac{20}{3}=-\frac{2}{3}$

Step3: Write final equation

Combine slope and y-intercept in $y=mx+b$:
$y=\frac{5}{3}x-\frac{2}{3}$

Answer:

$y=\frac{5}{3}x-\frac{2}{3}$