Question

Select the points that are part of the solution set for the inequality: y ≤ 2/5 x + 1. Select ALL that apply.
A. (10, 5.5)
B. (5, 3)
C. (10, 6)
D. (10, 4)

Answer 1

To determine which points are part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \), we will evaluate each point by substituting the x-value into the equation and checking if the resulting y-value satisfies the inequality.

1. **Point A: (10, 5.5)**
- Substitute \( x = 10 \):
\[
y \leq \frac{2}{5}(10) + 1 = \frac{20}{5} + 1 = 4 + 1 = 5
\]
- Check: \( 5.5 \leq 5 \) (FALSE)

2. **Point B: (5, 3)**
- Substitute \( x = 5 \):
\[
y \leq \frac{2}{5}(5) + 1 = \frac{10}{5} + 1 = 2 + 1 = 3
\]
- Check: \( 3 \leq 3 \) (TRUE)

3. **Point C: (10, 6)**
- Substitute \( x = 10 \):
\[
y \leq \frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
- Check: \( 6 \leq 5 \) (FALSE)

4. **Point D: (10, 4)**
- Substitute \( x = 10 \):
\[
y \leq \frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
- Check: \( 4 \leq 5 \) (TRUE)

Thus, the points that are part of the solution set for the inequality \( y \leq \frac{2}{5}x + 1 \) are:

- **B. (5, 3)**
- **D. (10, 4)**