Question

the solutions to the inequality $y > -3x + 2$ are shaded on the graph. which point is a solution? \\(\bigcirc\\ (0, 2)\\) \\(\bigcirc\\ (2, 0)\\) \\(\bigcirc\\ (1, -2)\\) \\(\bigcirc\\ (-2, 1)\\)

Explanation:

Step1: Test point (0,2)

Substitute $x=0, y=2$ into $y > -3x + 2$:
$2 > -3(0) + 2 \implies 2 > 2$ (False)

Step2: Test point (2,0)

Substitute $x=2, y=0$ into $y > -3x + 2$:
$0 > -3(2) + 2 \implies 0 > -6 + 2 \implies 0 > -4$ (True)

Step3: Test point (1,-2)

Substitute $x=1, y=-2$ into $y > -3x + 2$:
$-2 > -3(1) + 2 \implies -2 > -3 + 2 \implies -2 > -1$ (False)

Step4: Test point (-2,1)

Substitute $x=-2, y=1$ into $y > -3x + 2$:
$1 > -3(-2) + 2 \implies 1 > 6 + 2 \implies 1 > 8$ (False)

Answer:

B. (2, 0)