Question

Inequalities in Two Variables Quick Check
3 of 53 of 5 Items



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)
left parenthesis negative 10 comma 6 right parenthesis
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Answer 1

To determine which point is part of the solution set for the inequality \( y \leq 25x + 1 \), we can substitute the x-coordinates of each point into the inequality and see if the corresponding y-value is less than or equal to \( 25x + 1 \).

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

2. **Point (10, 6)**:
\[
y \leq 25(10) + 1 \\
6 \leq 250 + 1 \\
6 \leq 251 \quad \text{(True)}
\]

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

4. **Point (−10, 6)**:
\[
y \leq 25(-10) + 1 \\
6 \leq -250 + 1 \\
6 \leq -249 \quad \text{(False)}
\]

Based on these calculations, the points (10, 5.5), (10, 6), and (10, 4) are all part of the solution set for the inequality \( y \leq 25x + 1 \). However, the point (−10, 6) is not part of the solution set.

If you need to select only one response, you can choose any of (10, 5.5), (10, 6), or (10, 4), as all satisfy the inequality.