Show which of the following points is part of the solution set for the inequality y≤25x+1

Question

.(1 point)
Responses

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

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

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

(10,6)

Answer 1

To determine which point is part of the solution set for the inequality \( y \leq 25x + 1 \), we need to substitute each point into the inequality and check if the condition holds.

1. For the point \( (10, 4) \): \[ y = 4 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 250 + 1 = 251 \] Checking the inequality: \( 4 \leq 251 \) (True)

2. For the point \( (10, 5.5) \): \[ y = 5.5 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 250 + 1 = 251 \] Checking the inequality: \( 5.5 \leq 251 \) (True)

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

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

Now, summarizing the results:

• \( (10, 4) \) is a solution (True).
• \( (10, 5.5) \) is a solution (True).
• \( (-10, 6) \) is not a solution (False).
• \( (10, 6) \) is a solution (True).

The points \( (10, 4) \), \( (10, 5.5) \), and \( (10, 6) \) are part of the solution set.

Thus, the response is:

• (10, 4)
• (10, 5.5)
• (10, 6)

All of these points are part of the solution set.