Question

a line passes through the points (-2, -16) and (4, 20). 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 $(x_1,y_1)=(-2,-16)$ and $(x_2,y_2)=(4,20)$.
$m=\frac{20-(-16)}{4-(-2)}=\frac{36}{6}=6$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=6$ and point $(4,20)$.
$20=6\times4+b$
$20=24+b$
$b=20-24=-4$

Step3: Write final equation

Substitute $m=6$ and $b=-4$ into $y=mx+b$.
$y=6x-4$

Answer:

$y=6x-4$