Question

a line passes through the points (-1, -14) and (2, 13). 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 $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-1,-14)$ and $(x_2,y_2)=(2,13)$:
$m=\frac{13-(-14)}{2-(-1)}=\frac{27}{3}=9$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=9$ and $(x,y)=(2,13)$:
$13=9\times2+b$
$13=18+b$
$b=13-18=-5$

Step3: Write final equation

Substitute $m=9$ and $b=-5$ into $y=mx+b$.

Answer:

$y=9x-5$