Question

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

Explanation:

Step1: Check Point (2, 3)

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

Step2: Check Point (3, -2)

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

Step3: Check Point (2, 1)

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

Step4: Check Point (-1, 3)

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

Answer:

B. (3, -2)