Question

this is the graph of a linear inequality. write the inequality in slope-intercept form.

write your answer with y first, followed by an inequality symbol. use integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Find line slope

First, identify two points on the line: $(-8, 0)$ and $(0, 2)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{2-0}{0-(-8)}=\frac{2}{8}=\frac{1}{4}$

Step2: Get slope-intercept line equation

Slope-intercept form: $y=mx+b$, where $b=2$ (y-intercept).
$y=\frac{1}{4}x+2$

Step3: Determine inequality symbol

The shaded area is above the solid line, so use $\geq$.

Answer:

$y\geq\frac{1}{4}x+2$