Question

What is part of the solution set of Y ≤ 2/5x + 1

-10, 6

10, 6

10, 4

10, 5.5

Answers

GPT-4o mini
To determine which points are part of the solution set for the inequality \(Y \leq \frac{2}{5}x + 1\), we can substitute each point into the inequality and see if the inequality holds true.

1. **For the point (-10, 6)**:
\[
6 \leq \frac{2}{5}(-10) + 1
\]
\[
6 \leq -4 + 1
\]
\[
6 \leq -3 \quad \text{(False)}
\]

2. **For the point (10, 6)**:
\[
6 \leq \frac{2}{5}(10) + 1
\]
\[
6 \leq 4 + 1
\]
\[
6 \leq 5 \quad \text{(False)}
\]

3. **For the point (10, 4)**:
\[
4 \leq \frac{2}{5}(10) + 1
\]
\[
4 \leq 4 + 1
\]
\[
4 \leq 5 \quad \text{(True)}
\]

4. **For the point (10, 5.5)**:
\[
5.5 \leq \frac{2}{5}(10) + 1
\]
\[
5.5 \leq 4 + 1
\]
\[
5.5 \leq 5 \quad \text{(False)}
\]

The only point that satisfies the inequality \(Y \leq \frac{2}{5}x + 1\) is (10, 4). Therefore, the part of the solution set is:

**(10, 4)**.