Question

which inequality matches the picture shown?

$y\geq -\frac{1}{2}x + 5$

$y > -\frac{1}{2}x + 5$

$y < -\frac{1}{2}x + 5$

$y\leq -\frac{1}{2}x + 5$

Explanation:

Step1: Identify line equation

The line has slope $-\frac{1}{2}$ and y-intercept $5$, so its equation is $y = -\frac{1}{2}x + 5$.

Step2: Check line style

The line is solid, so the inequality uses $\leq$ or $\geq$.

Step3: Test shading direction

Pick a test point (e.g., $(0,0)$):
Substitute into $y \leq -\frac{1}{2}x + 5$:
$0 \leq -\frac{1}{2}(0) + 5$
$0 \leq 5$, which is true. The shaded region includes $(0,0)$, so the inequality is $y \leq -\frac{1}{2}x + 5$.

Answer:

$\boldsymbol{y \leq -\frac{1}{2}x + 5}$