Question

Which of the following points is a part of the solution set for the inequality y≥3x−1 ?(1 point)
Responses

(−1,−5)
left parenthesis negative 1 comma negative 5 right parenthesis

(2,5)
left parenthesis 2 comma 5 right parenthesis

(−2.5,−9)
left parenthesis negative 2.5 comma negative 9 right parenthesis

(1,1)

Answer 1

To determine which of the given points is part of the solution set for the inequality \( y \geq 3x - 1 \), we'll evaluate each point by substituting the \( x \) coordinate into the inequality and checking if the \( y \) coordinate satisfies it.

1. For the point \( (-1, -5) \):
\[
y \geq 3x - 1 \\
-5 \geq 3(-1) - 1 \\
-5 \geq -3 - 1 \\
-5 \geq -4 \quad \text{(False)}
\]

2. For the point \( (2, 5) \):
\[
y \geq 3x - 1 \\
5 \geq 3(2) - 1 \\
5 \geq 6 - 1 \\
5 \geq 5 \quad \text{(True)}
\]

3. For the point \( (-2.5, -9) \):
\[
y \geq 3x - 1 \\
-9 \geq 3(-2.5) - 1 \\
-9 \geq -7.5 - 1 \\
-9 \geq -8.5 \quad \text{(False)}
\]

4. For the point \( (1, 1) \):
\[
y \geq 3x - 1 \\
1 \geq 3(1) - 1 \\
1 \geq 3 - 1 \\
1 \geq 2 \quad \text{(False)}
\]

The only point that satisfies the inequality \( y \geq 3x - 1 \) is \( (2, 5) \).

So, the point that is part of the solution set for the inequality is **(2, 5)**.