Question

a line passes through the points (-2, -1) and (6, 1). 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 $(x_1,y_1)=(-2,-1)$ and $(x_2,y_2)=(6,1)$.
$m=\frac{1-(-1)}{6-(-2)}=\frac{2}{8}=\frac{1}{4}$

Step2: Find y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=\frac{1}{4}$ and point $(-2,-1)$:
$-1=\frac{1}{4}(-2)+b$
$-1=-\frac{1}{2}+b$
$b=-1+\frac{1}{2}=-\frac{1}{2}$

Step3: Write final equation

Substitute $m=\frac{1}{4}$ and $b=-\frac{1}{2}$ into $y=mx+b$.

Answer:

$y=\frac{1}{4}x-\frac{1}{2}$