Question

which ordered pair is a solution of the inequality shown in the graph? (-1, -1) (-1, 3) (2, -2) (1, 0)

Explanation:

Step1: Find line equation

The line passes through (0,1) and (1,-1). Slope $m=\frac{-1-1}{1-0}=-2$. Equation: $y=-2x+1$.

Step2: Determine inequality

Shaded region is below the solid line, so $y\leq -2x+1$.

Step3: Test (-1,-1)

Substitute $x=-1,y=-1$: $-1\leq -2(-1)+1 \implies -1\leq 3$, which is true.

Step4: Test other options

For (-1,3): $3\leq -2(-1)+1 \implies 3\leq 3$? No, 3=3 but point is above shaded area.
For (2,-2): $-2\leq -2(2)+1 \implies -2\leq -3$, false.
For (1,0): $0\leq -2(1)+1 \implies 0\leq -1$, false.

Answer:

(-1, -1)