Select the points that are part of the solution set for the inequality y≤25x+1

Question

. 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

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 2

The inequality is y leq 2/5x + 1

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:

• \((10, 4)\)
• \((5, 3)\)