Question

choose the correct inequality for this graph.
y > -x + 2
y ≥ -x + 2
y < -x + 2
y ≤ -x + 2

Explanation:

Step1: Identify boundary line equation

The line has slope $-1$ and y-intercept $2$, so equation is $y=-x+2$.

Step2: Check line style (dashed/solid)

The line is dashed, so inequality uses $>$ or $<$.

Step3: Test a point in shaded region

Use $(0,0)$: $0 > -0+2$? No. Use $(0,3)$: $3 > -0+2$? Yes. So inequality is $y > -x+2$.

Answer:

$y > -x + 2$