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 (10,4) left parenthesis 10 comma 4 right parenthesis (10,5.5) left parenthesis 10 comma 5.5 right parenthesis (10,6) left parenthesis 10 comma 6 right parenthesis

Answer 1

To determine which points are part of the solution set for the inequality \( y \leq 25x + 1 \), we can substitute the x-values of each point into the equation and check if the corresponding y-value meets the condition of the inequality.

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

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

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

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

From the analysis above:
- The point \((-10, 6)\) is **not** part of the solution set.
- The points \((10, 4)\), \((10, 5.5)\), and \((10, 6)\) **are** part of the solution set.

Thus, the points that are part of the solution set for the inequality are \((10, 4)\), \((10, 5.5)\), and \((10, 6)\).