Question

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

Explanation:

Step1: Recall the inequality

The inequality is \( y \leq -x + 1 \). We need to check each point by substituting \( x \) and \( y \) into the inequality.

Step2: Check point (2, 3)

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

Step3: Check point (3, -7)

Substitute \( x = 3 \), \( y = -7 \) into \( y \leq -x + 1 \):
\( -7 \leq -3 + 1 \) → \( -7 \leq -2 \). This is true.

Step4: Check point (2, 1)

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

Step5: Check point (-1, 3)

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

Answer:

(3, -7)