Question

a line passes through the points (-19, -16) and (2, 2). 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 $(x_1,y_1)=(-19,-16)$ and $(x_2,y_2)=(2,2)$:
$m=\frac{2-(-16)}{2-(-19)}=\frac{18}{21}=\frac{6}{7}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=\frac{6}{7}$ and point $(2,2)$:
$2=\frac{6}{7}(2)+b$
$2=\frac{12}{7}+b$
$b=2-\frac{12}{7}=\frac{14}{7}-\frac{12}{7}=\frac{2}{7}$

Step3: Write final equation

Substitute $m=\frac{6}{7}$ and $b=\frac{2}{7}$ into $y=mx+b$.

Answer:

$y=\frac{6}{7}x+\frac{2}{7}$