Question

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

Answer 1

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

1. **Point (2, 5)**:
\[
y \geq 3x - 1 \quad \text{becomes} \quad 5 \geq 3(2) - 1
\]
\[
5 \geq 6 - 1
\]
\[
5 \geq 5 \quad \text{(True)}
\]

2. **Point (1, 1)**:
\[
y \geq 3x - 1 \quad \text{becomes} \quad 1 \geq 3(1) - 1
\]
\[
1 \geq 3 - 1
\]
\[
1 \geq 2 \quad \text{(False)}
\]

3. **Point (−1, −5)**:
\[
y \geq 3x - 1 \quad \text{becomes} \quad -5 \geq 3(-1) - 1
\]
\[
-5 \geq -3 - 1
\]
\[
-5 \geq -4 \quad \text{(False)}
\]

4. **Point (−2.5, −9)**:
\[
y \geq 3x - 1 \quad \text{becomes} \quad -9 \geq 3(-2.5) - 1
\]
\[
-9 \geq -7.5 - 1
\]
\[
-9 \geq -8.5 \quad \text{(False)}
\]

From the evaluations above, the only point that is a part of the solution set for the inequality \( y \geq 3x - 1 \) is:

**(2, 5)**.