Question

which inequality is graphed?
$y \geq \frac{1}{4}x - 1$
$y < \frac{1}{4}x - 1$
$y > \frac{1}{4}x - 1$

Explanation:

Step1: Identify line equation

The line has y-intercept $-1$, slope $\frac{1}{4}$, so equation is $y=\frac{1}{4}x-1$. It is a solid line, so inequality uses $\geq$ or $\leq$.

Step2: Test a point for shading

Test $(0,0)$: $\frac{1}{4}(0)-1=-1$. $0 \geq -1$ is true, and $(0,0)$ is in the shaded region.

Answer:

$y \geq \frac{1}{4}x - 1$