Question

Show which of the following points is part of the solution set for the inequality y≤25x+1 .(1 point)%0D%0AResponses%0D%0A%0D%0A(10,5.5)%0D%0Aleft parenthesis 10 comma 5.5 right parenthesis%0D%0A%0D%0A(−10,6)%0D%0Aleft parenthesis negative 10 comma 6 right parenthesis%0D%0A%0D%0A(10,6)%0D%0Aleft parenthesis 10 comma 6 right parenthesis%0D%0A%0D%0A(10,4

Answer 1

To determine which points are part of the solution set for the inequality \( y \leq 25x + 1 \), we will substitute the x-values from each point into the equation \( y = 25x + 1 \) and check if the y-value of the point is less than or equal to the result.

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

2. **For the point (−10, 6)**:
\[
y = 25(-10) + 1 = -250 + 1 = -249
\]
\[
6 \leq -249 \quad \text{(False)}
\]

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

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

The points (10, 5.5), (10, 6), and (10, 4) are all part of the solution set for the inequality \( y \leq 25x + 1 \), while the point (−10, 6) is not.

So, the points that satisfy the inequality are:
- (10, 5.5)
- (10, 6)
- (10, 4)

**Answer: (10, 5.5), (10, 6), and (10, 4) are part of the solution set.**