Question

Select the points that are part of the solution set for the inequality y ≤ 2/5 x + 1
. Select ALL that apply.(2 points)
Responses

(5, 3)
(5, 3)

(10, 4)
(10, 4)

(10, 6)
(10, 6)

(10, 5.5)

Answer 1

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

1. **Point (5, 3)**:
- Calculate \( y = \frac{2}{5}(5) + 1 \):
\[
y = 2 + 1 = 3
\]
- Since \( 3 \leq 3 \), the point (5, 3) is in the solution set.

2. **Point (10, 4)**:
- Calculate \( y = \frac{2}{5}(10) + 1 \):
\[
y = 4 + 1 = 5
\]
- Since \( 4 \leq 5 \), the point (10, 4) is in the solution set.

3. **Point (10, 6)**:
- Calculate \( y = \frac{2}{5}(10) + 1 \):
\[
y = 5
\]
- Since \( 6 \leq 5 \) is false, the point (10, 6) is not in the solution set.

4. **Point (10, 5.5)**:
- Calculate \( y = \frac{2}{5}(10) + 1 \):
\[
y = 5
\]
- Since \( 5.5 \leq 5 \) is false, the point (10, 5.5) is not in the solution set.

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

- (5, 3)
- (10, 4)

So the answers are:
- (5, 3)
- (10, 4)