Question

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

Explanation:

Step1: Find line equation

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

Step2: Identify inequality direction

The shaded region is above the solid line, so inequality is $y\geq\frac{1}{2}x$

Step3: Test (-1,-1)

Substitute $x=-1,y=-1$: $-1\geq\frac{1}{2}(-1) \implies -1\geq-0.5$, False

Step4: Test (1,0)

Substitute $x=1,y=0$: $0\geq\frac{1}{2}(1) \implies 0\geq0.5$, False

Step5: Test (2,-2)

Substitute $x=2,y=-2$: $-2\geq\frac{1}{2}(2) \implies -2\geq1$, False

Step6: Test (-1,3)

Substitute $x=-1,y=3$: $3\geq\frac{1}{2}(-1) \implies 3\geq-0.5$, True

Answer:

(-1, 3)