Question

Show which of the following points is part of the solution set for the inequality y≤2/5x+1.(1 point)
Responses

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

(−10,6)
left parenthesis negative 10 comma 6 right parenthesis

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

(10,5.5)

Answer 1

To determine which of the given points satisfies the inequality \( y \leq \frac{2}{5}x + 1 \), we need to plug in the x-coordinates of each point into the inequality and see if the corresponding y-coordinates satisfy it.

1. **Point (10, 4)**:
- Calculate the right-hand side:
\[
\frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
- Check the inequality:
\[
4 \leq 5 \quad \text{(True)}
\]

2. **Point (−10, 6)**:
- Calculate the right-hand side:
\[
\frac{2}{5}(-10) + 1 = -4 + 1 = -3
\]
- Check the inequality:
\[
6 \leq -3 \quad \text{(False)}
\]

3. **Point (10, 6)**:
- Calculate the right-hand side:
\[
\frac{2}{5}(10) + 1 = 5 + 1 = 6
\]
- Check the inequality:
\[
6 \leq 6 \quad \text{(True)}
\]

4. **Point (10, 5.5)**:
- Calculate the right-hand side:
\[
\frac{2}{5}(10) + 1 = 5 + 1 = 6
\]
- Check the inequality:
\[
5.5 \leq 6 \quad \text{(True)}
\]

**Summary**:
- (10, 4) → true
- (−10, 6) → false
- (10, 6) → true
- (10, 5.5) → true

Therefore, the points **(10, 4)**, **(10, 6)**, and **(10, 5.5)** are part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \). The only point that is **not** in the solution set is **(−10, 6)**.