Question

Select the points that are part of the solution set for the inequality y≤25x+1
. Select ALL that apply.(2 points)
Responses

(10, 5.5)
(10, 5.5)

(10, 6)
(10, 6)

(10, 4)
(10, 4)

(5, 3)

Answer 1

The inequality is y leq 2/5x + 1

Answer 2

To determine which points are part of the solution set for the inequality \( y \leq 25x + 1 \), we need to evaluate each point by plugging in its coordinates into the inequality.

1. For the point \((10, 5.5)\):
\[
y = 5.5 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 250 + 1 = 251
\]
\[
5.5 \leq 251 \quad \text{(True)}
\]

2. For the point \((10, 6)\):
\[
y = 6 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 250 + 1 = 251
\]
\[
6 \leq 251 \quad \text{(True)}
\]

3. For the point \((10, 4)\):
\[
y = 4 \quad \text{and} \quad 25x + 1 = 25(10) + 1 = 250 + 1 = 251
\]
\[
4 \leq 251 \quad \text{(True)}
\]

4. For the point \((5, 3)\):
\[
y = 3 \quad \text{and} \quad 25x + 1 = 25(5) + 1 = 125 + 1 = 126
\]
\[
3 \leq 126 \quad \text{(True)}
\]

All four points satisfy the inequality \( y \leq 25x + 1 \):

- \((10, 5.5)\)
- \((10, 6)\)
- \((10, 4)\)
- \((5, 3)\)

Thus, all points are part of the solution set for the inequality.

Answer 3

Let's evaluate the points with the corrected inequality \(y \leq \frac{2}{5}x + 1\).

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

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

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

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

### Summary of Results:
- **\((10, 5.5)\)**: False
- **\((10, 6)\)**: False
- **\((10, 4)\)**: True
- **\((5, 3)\)**: True

### Points that are part of the solution set:
- \((10, 4)\)
- \((5, 3)\)

So the correct responses to the inequality \(y \leq \frac{2}{5}x + 1\) are:
- \((10, 4)\)
- \((5, 3)\)