Show which of the following points is part of the solution set for the inequality y≤25x+1 .(1 point) Responses (10,6) left parenthesis 10 comma 6 right parenthesis (10,5.5) left parenthesis 10 comma 5.5 right parenthesis (−10,6) left parenthesis negative 10 comma 6 right parenthesis (10,4)

1 answer

To determine which of the given points is part of the solution set for the inequality \( y \leq 25x + 1 \), we will substitute each point into the inequality and check if it holds true.

  1. For (10, 6): \[ y = 6 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 250 + 1 = 251 \] Check: \( 6 \leq 251 \) (True)

  2. For (10, 5.5): \[ y = 5.5 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 251 \] Check: \( 5.5 \leq 251 \) (True)

  3. For (−10, 6): \[ y = 6 \quad \text{and} \quad 25x + 1 = 25(-10) + 1 = -250 + 1 = -249 \] Check: \( 6 \leq -249 \) (False)

  4. For (10, 4): \[ y = 4 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 251 \] Check: \( 4 \leq 251 \) (True)

So, the points that are part of the solution set for the inequality \( y \leq 25x + 1 \) are (10, 6), (10, 5.5), and (10, 4).

The answer is:

  • (10, 6)
  • (10, 5.5)
  • (10, 4)

Only (−10, 6) is not a solution.