Question

Which of the following points is a part of the solution
set for the inequality 𝑦 ≥ 3𝑥 − 1
(1, 1)
(-1, -5)
(2, 5)
(-2.5, -9

Answer 1

To determine which points are part of the solution set for the inequality \(y \geq 3x - 1\), we can substitute each point into the inequality and check if it holds true.

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

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

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

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

The only point that satisfies the inequality \(y \geq 3x - 1\) is \((2, 5)\). Therefore, the point \((2, 5)\) is a part of the solution set for the inequality.