Question

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

Answer 1

To determine which of the given points is part of the solution set for the inequality \( y \leq 25x + 1 \), we can substitute each point into the inequality.

1. **Point (10, 5.5)**:
- Substitute \( x = 10 \) and \( y = 5.5 \):
\[
5.5 \leq 25(10) + 1 \\
5.5 \leq 250 + 1 \\
5.5 \leq 251 \quad \text{(True)}
\]

2. **Point (-10, 6)**:
- Substitute \( x = -10 \) and \( y = 6 \):
\[
6 \leq 25(-10) + 1 \\
6 \leq -250 + 1 \\
6 \leq -249 \quad \text{(False)}
\]

3. **Point (10, 4)**:
- Substitute \( x = 10 \) and \( y = 4 \):
\[
4 \leq 25(10) + 1 \\
4 \leq 250 + 1 \\
4 \leq 251 \quad \text{(True)}
\]

4. **Point (10, 6)**:
- Substitute \( x = 10 \) and \( y = 6 \):
\[
6 \leq 25(10) + 1 \\
6 \leq 250 + 1 \\
6 \leq 251 \quad \text{(True)}
\]

Now let's summarize the results:
- Point (10, 5.5) - **True**
- Point (-10, 6) - **False**
- Point (10, 4) - **True**
- Point (10, 6) - **True**

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