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 $y = -x + 2$. The solid line means $\leq$ or $\geq$.

Step2: Test a point for inequality direction

Test $(0,0)$: substitute into $y \square -x + 2$ gives $0 \square 2$. Since the shaded region includes $(0,0)$, use $\leq$. Final inequality: $y \leq -x + 2$

Answer:

$\boldsymbol{y \leq -x + 2}$