Show which of the following points is part of the solution set for the inequality y≤2/5x+1

.(1 point)
Responses

(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis

(10,6)
left parenthesis 10 comma 6 right parenthesis

(10,4)
left parenthesis 10 comma 4 right parenthesis

(−10,6)

1 answer

To determine which of the given points is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we can substitute each point into the inequality.

  1. Check (10, 5.5): \[ y = 5.5, \quad x = 10 \] Substitute into the inequality: \[ 5.5 \leq \frac{2}{5}(10) + 1 \] \[ 5.5 \leq 4 + 1 \] \[ 5.5 \leq 5 \] False

  2. Check (10, 6): \[ y = 6, \quad x = 10 \] Substitute into the inequality: \[ 6 \leq \frac{2}{5}(10) + 1 \] \[ 6 \leq 4 + 1 \] \[ 6 \leq 5 \] False

  3. Check (10, 4): \[ y = 4, \quad x = 10 \] Substitute into the inequality: \[ 4 \leq \frac{2}{5}(10) + 1 \] \[ 4 \leq 4 + 1 \] \[ 4 \leq 5 \] True

  4. Check (−10, 6): \[ y = 6, \quad x = -10 \] Substitute into the inequality: \[ 6 \leq \frac{2}{5}(-10) + 1 \] \[ 6 \leq -4 + 1 \] \[ 6 \leq -3 \] False

The only point that is part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \) is (10, 4).