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 of the given points is part of the solution set for the inequality \( y \leq 25x + 1 \), we will substitute the x and y coordinates of each point into the inequality and check if it holds true.

1. For the point \( (-10, 6) \):
\[
y \leq 25x + 1 \implies 6 \leq 25(-10) + 1 \implies 6 \leq -250 + 1 \implies 6 \leq -249 \quad \text{(False)}
\]

2. For the point \( (10, 5.5) \):
\[
y \leq 25x + 1 \implies 5.5 \leq 25(10) + 1 \implies 5.5 \leq 250 + 1 \implies 5.5 \leq 251 \quad \text{(True)}
\]

3. For the point \( (10, 6) \):
\[
y \leq 25x + 1 \implies 6 \leq 25(10) + 1 \implies 6 \leq 250 + 1 \implies 6 \leq 251 \quad \text{(True)}
\]

4. For the point \( (10, 4) \):
\[
y \leq 25x + 1 \implies 4 \leq 25(10) + 1 \implies 4 \leq 250 + 1 \implies 4 \leq 251 \quad \text{(True)}
\]

Thus, the points \( (10, 5.5) \), \( (10, 6) \), and \( (10, 4) \) are all part of the solution set for the inequality, while \( (-10, 6) \) is not.

Therefore, the points that are part of the solution set are:
- \( (10, 5.5) \)
- \( (10, 6) \)
- \( (10, 4) \)