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

(−10,6)
left parenthesis negative 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

Answer 1

To determine which of the given points is part of the solution set for the inequality \( y \leq 25x + 1 \), we need to substitute each point into the inequality and see if it holds true.

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

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

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

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

Thus, the points \((10, 6)\), \((10, 4)\), and \((10, 5.5)\) are part of the solution set, while \((-10, 6)\) is not.

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