Question

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

Explanation:

Step1: Test point (2, 3)

Substitute \(x = 2\), \(y = 3\) into \(y\leq -x + 1\):
\(3\leq -2 + 1\) → \(3\leq -1\), false.

Step2: Test point (3, -2)

Substitute \(x = 3\), \(y = -2\) into \(y\leq -x + 1\):
\(-2\leq -3 + 1\) → \(-2\leq -2\), true.

Step3: Test point (2, 1)

Substitute \(x = 2\), \(y = 1\) into \(y\leq -x + 1\):
\(1\leq -2 + 1\) → \(1\leq -1\), false.

Step4: Test point (-1, 3)

Substitute \(x = -1\), \(y = 3\) into \(y\leq -x + 1\):
\(3\leq 1 + 1\) → \(3\leq 2\), false.

Answer:

B. (3, -2)