Question

find an equation for the line below.

Explanation:

Step1: Identify two points

The marked points are $(-3, -5)$ and $(1, -3)$.

Step2: Calculate slope $m$

Use slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$\displaystyle m=\frac{-3 - (-5)}{1 - (-3)}=\frac{2}{4}=\frac{1}{2}$

Step3: Find y-intercept $b$

Substitute $m=\frac{1}{2}$ and $(1, -3)$ into $y=mx+b$:
$-3=\frac{1}{2}(1)+b$
Solve for $b$: $b=-3-\frac{1}{2}=-\frac{7}{2}$

Step4: Write line equation

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

Answer:

$\displaystyle y=\frac{1}{2}x-\frac{7}{2}$