Question

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

Explanation:

Step1: Find slope of boundary line

The line passes through $(0,4)$ and $(-2,-4)$. Slope $m=\frac{-4-4}{-2-0}=\frac{-8}{-2}=4$

Step2: Identify y-intercept

The line crosses the y-axis at $(0,4)$, so $b=4$. The line equation is $y=4x+4$.

Step3: Determine inequality symbol

The boundary line is solid, and the shaded region is to the left of the line (test point $(0,0)$: $0 < 4(0)+4$ is true, and $(0,0)$ is in the shaded area). So use $\leq$.

Answer:

$y \leq 4x + 4$