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 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 need to substitute each point into the inequality and see if it holds true.

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

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

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

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

The points \( (10, 5.5) \), \( (10, 6) \), and \( (10, 4) \) are all part of the solution set because they satisfy the inequality. However, \( (-10, 6) \) does not satisfy the inequality.

Thus, the options \( (10, 5.5) \), \( (10, 6) \), and \( (10, 4) \) are all valid solutions.