Question

2-Variable Equations & Inequalities Online Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Which of the following points is a part of the solution set for the inequality y≥3x−1
?(1 point)
Responses

(1,1)
left parenthesis 1 comma 1 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,−5)
left parenthesis negative 1 comma negative 5 right parenthesis
Remaining Attempts : 3
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Answer 1

To determine which of the following points is part of the solution set for the inequality \( y \geq 3x - 1 \), we will substitute the x-coordinates of each point into the equation \( y = 3x - 1 \) and check if the corresponding y-values satisfy the inequality.

1. **For the point (1, 1):**
\[
y = 3(1) - 1 = 3 - 1 = 2
\]
Check the inequality:
\[
1 \geq 2 \quad \text{(False)}
\]

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

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

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

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

**(2, 5)**