Question

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

Answer 1

To determine which points are part of the solution set for the inequality \( y < \frac{2}{5}x + 1 \), we need to evaluate each given point by substituting the \( x \) value into the equation \( y = \frac{2}{5}x + 1 \) and then checking if the \( y \) value of the point is less than the calculated \( y \) value.

1. **Point A: (10, 4)**
\[
y = \frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check: \( 4 < 5 \) (True)

2. **Point B: (10, 6)**
\[
y = \frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check: \( 6 < 5 \) (False)

3. **Point C: (5, 3)**
\[
y = \frac{2}{5}(5) + 1 = 2 + 1 = 3
\]
Check: \( 3 < 3 \) (False)

4. **Point D: (10, 5.5)**
\[
y = \frac{2}{5}(10) + 1 = 4 + 1 = 5
\]
Check: \( 5.5 < 5 \) (False)

Now let's summarize:

- **A. (10, 4)** is part of the solution set.
- **B. (10, 6)** is not part of the solution set.
- **C. (5, 3)** is not part of the solution set.
- **D. (10, 5.5)** is not part of the solution set.

Thus, the only point that is part of the solution set is **A. (10, 4)**.