Select the points that are part of the solution set for the inequality y≤25x+1

Question

. Select ALL that apply.(2 points)
Responses

(5, 3)
(5, 3)

(10, 5.5)
(10, 5.5)

(10, 6)
(10, 6)

(10, 4)

Answer 1

To determine which points satisfy the inequality \( y \leq 25x + 1 \), we need to evaluate each given point by substituting its coordinates into the inequality.

Let's evaluate each point:

1. For the point (5, 3):

   • Substitute: \( y = 3 \), \( x = 5 \)
   • Check: \( 3 \leq 25(5) + 1 \)
   • Calculate: \( 3 \leq 125 + 1 \) → \( 3 \leq 126 \) (True)

2. For the point (10, 5.5):

   • Substitute: \( y = 5.5 \), \( x = 10 \)
   • Check: \( 5.5 \leq 25(10) + 1 \)
   • Calculate: \( 5.5 \leq 250 + 1 \) → \( 5.5 \leq 251 \) (True)

3. For the point (10, 6):

   • Substitute: \( y = 6 \), \( x = 10 \)
   • Check: \( 6 \leq 25(10) + 1 \)
   • Calculate: \( 6 \leq 250 + 1 \) → \( 6 \leq 251 \) (True)

4. For the point (10, 4):

   • Substitute: \( y = 4 \), \( x = 10 \)
   • Check: \( 4 \leq 25(10) + 1 \)
   • Calculate: \( 4 \leq 250 + 1 \) → \( 4 \leq 251 \) (True)

Since all calculations are true, all the points provided satisfy the inequality \( y \leq 25x + 1 \).

The solution set includes all points:

• (5, 3)
• (10, 5.5)
• (10, 6)
• (10, 4)