Question

Show which of the following points is part of the solution set for the inequality y≤25x+1.(1 point)
Responses

(10,5.5)
left parenthesis 10 comma 5.5 right parenthesis

(10,6)
left parenthesis 10 comma 6 right parenthesis

(10,4)
left parenthesis 10 comma 4 right parenthesis

(−10,6)
left parenthesis negative 10 comma 6 right parenthesis

Answer 1

which one

Answer 2

To determine which of the given points satisfies the inequality \( y \leq 25x + 1 \), we need to substitute the x-value of each point into the equation \( y = 25x + 1 \) and see if the corresponding y-value is less than or equal to the calculated value.

1. **For the point (10, 5.5)**:
- \( x = 10 \)
- Calculate \( y = 25(10) + 1 = 250 + 1 = 251 \)
- Check: \( 5.5 \leq 251 \) (True)

2. **For the point (10, 6)**:
- \( x = 10 \)
- Calculate \( y = 25(10) + 1 = 250 + 1 = 251 \)
- Check: \( 6 \leq 251 \) (True)

3. **For the point (10, 4)**:
- \( x = 10 \)
- Calculate \( y = 25(10) + 1 = 250 + 1 = 251 \)
- Check: \( 4 \leq 251 \) (True)

4. **For the point (−10, 6)**:
- \( x = -10 \)
- Calculate \( y = 25(-10) + 1 = -250 + 1 = -249 \)
- Check: \( 6 \leq -249 \) (False)

Based on this analysis, all points except for (−10, 6) satisfy the inequality \( y \leq 25x + 1 \). Therefore, the points that are part of the solution set are (10, 5.5), (10, 6), and (10, 4).

Answer 3

Among the given points, we need to select just one point that satisfies the inequality \( y \leq 25x + 1 \).

After evaluating the points:

1. **(10, 5.5)**: Satisfies the inequality.
2. **(10, 6)**: Satisfies the inequality.
3. **(10, 4)**: Satisfies the inequality.
4. **(−10, 6)**: Does not satisfy the inequality.

Since all three of the first points satisfy the inequality, you can choose any one of them.

If you need to pick just **one point**, you could choose:

**(10, 5.5)**.

This is a valid point in the solution set for the inequality.