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 negative 10 comma 6 right parenthesis

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

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

(10,4)

Answer 1

To determine which points satisfy the inequality \( y \leq 25x + 1 \), we need to substitute the \( x \) values of each point into the inequality and check if the corresponding \( y \) value is less than or equal to \( 25x + 1 \).

1. **Check (−10, 6)**:
- Substitute \( x = -10 \):
\[
y \leq 25(-10) + 1 \\
y \leq -250 + 1 \\
y \leq -249
\]
- Since \( 6 > -249 \), this point does not satisfy the inequality.

2. **Check (10, 5.5)**:
- Substitute \( x = 10 \):
\[
y \leq 25(10) + 1 \\
y \leq 250 + 1 \\
y \leq 251
\]
- Since \( 5.5 < 251 \), this point satisfies the inequality.

3. **Check (10, 6)**:
- Substitute \( x = 10 \):
\[
y \leq 25(10) + 1 \\
y \leq 250 + 1 \\
y \leq 251
\]
- Since \( 6 < 251 \), this point satisfies the inequality.

4. **Check (10, 4)**:
- Substitute \( x = 10 \):
\[
y \leq 25(10) + 1 \\
y \leq 250 + 1 \\
y \leq 251
\]
- Since \( 4 < 251 \), this point satisfies the inequality.

**Conclusion**: The points (10, 5.5), (10, 6), and (10, 4) are part of the solution set for the inequality \( y \leq 25x + 1 \). However, for a single point selection, any of these three points would be correct.