Is (4, 7) a solution to the inequality y < - ¾ x - 5?

1 answer

To determine if the point (4, 7) is a solution to the inequality \( y < -\frac{3}{4}x - 5 \), we can substitute \( x = 4 \) and \( y = 7 \) into the inequality.

  1. Substitute \( x = 4 \) into the inequality: \[ y < -\frac{3}{4}(4) - 5 \]

  2. Calculate the right side: \[ -\frac{3}{4}(4) = -3 \] So the inequality becomes: \[ y < -3 - 5 \] Simplifying further gives: \[ y < -8 \]

  3. Now substitute \( y = 7 \) into the inequality: \[ 7 < -8 \]

This statement is false. Therefore, (4, 7) is not a solution to the inequality \( y < -\frac{3}{4}x - 5 \).