Question

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

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

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

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

(−10,6)

Answer 1

To determine which of the given points is part of the solution set for the inequality \( y \leq 25x + 1 \), we can substitute the x-coordinates of each point into the equation and check if the corresponding y-coordinates satisfy the inequality.

1. **For the point \((10, 6)\):**
\[
y = 25(10) + 1 = 250 + 1 = 251
\]
Check if \( 6 \leq 251 \): **True.**

2. **For the point \((10, 4)\):**
\[
y = 25(10) + 1 = 250 + 1 = 251
\]
Check if \( 4 \leq 251 \): **True.**

3. **For the point \((10, 5.5)\):**
\[
y = 25(10) + 1 = 250 + 1 = 251
\]
Check if \( 5.5 \leq 251 \): **True.**

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

Thus, the points \((10, 6)\), \((10, 4)\), and \((10, 5.5)\) all satisfy the inequality \( y \leq 25x + 1 \), but \((-10, 6)\) does not.

Since multiple points satisfy the inequality, you can choose any of those points. If you need to select just one, any of \((10, 6)\), \((10, 4)\), or \((10, 5.5)\) would be acceptable as part of the solution set.