Question

a line passes through the points (-12, -16) and (2, 12). 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 $(x_1,y_1)=(-12,-16)$ and $(x_2,y_2)=(2,12)$.
$m=\frac{12-(-16)}{2-(-12)}=\frac{12+16}{2+12}=\frac{28}{14}=2$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=2$, $(x,y)=(2,12)$:
$12=2\times2+b$
$12=4+b$
$b=12-4=8$

Step3: Write final equation

Substitute $m=2$ and $b=8$ into $y=mx+b$.

Answer:

$y=2x+8$