Question

determine the equation of the line that passes through the points (-2, -12) and (4, 15). enter your answer in slope-intercept form $y = mx + b$.

Explanation:

Step1: Calculate the slope $m$

Use slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ with $(x_1,y_1)=(-2,-12)$ and $(x_2,y_2)=(4,15)$
$m=\frac{15-(-12)}{4-(-2)}=\frac{27}{6}=\frac{9}{2}$

Step2: Solve for y-intercept $b$

Substitute $m=\frac{9}{2}$ and $(x,y)=(-2,-12)$ into $y=mx+b$
$-12=\frac{9}{2}(-2)+b$
$-12=-9+b$
$b=-12+9=-3$

Step3: Write slope-intercept equation

Combine $m=\frac{9}{2}$ and $b=-3$ into $y=mx+b$

Answer:

$y=\frac{9}{2}x-3$