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 type

The graph has a dashed line, so the inequality uses $>$ or $<$ (no equality).

Step2: Find line equation

The line follows $y = -\frac{1}{2}x + 5$ (slope $-\frac{1}{2}$, y-intercept 5).

Step3: Test shading direction

Pick a point in the shaded area, e.g., $(0,6)$:
Substitute into $y > -\frac{1}{2}x + 5$:
$6 > -\frac{1}{2}(0) + 5$
$6 > 5$, which is true.

Step4: Confirm correct inequality

The dashed line and correct shaded region match $y > -\frac{1}{2}x + 5$.

Answer:

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