Question

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)

Answer 1

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.