Question
Which of the following ordered pairs is part of the solution set for the equation y=2.5x−2?Option #1: (−2,0)Option #2: (2,5)Option #3: (2,3)
Answers
GPT-4o mini
To determine which ordered pair is part of the solution set for the equation \( y = 2.5x - 2 \), we can substitute the x-value from each ordered pair into the equation and see if the resulting y-value matches the y-value from the ordered pair.
**Option #1: (−2,0)**
- Substitute \( x = -2 \):
\[
y = 2.5(-2) - 2 = -5 - 2 = -7
\]
The ordered pair is (−2, 0), and since \( 0 \neq -7 \), this pair is not a solution.
**Option #2: (2,5)**
- Substitute \( x = 2 \):
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is (2, 5), and since \( 5 \neq 3 \), this pair is not a solution.
**Option #3: (2,3)**
- Substitute \( x = 2 \):
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is (2, 3), and since \( 3 = 3 \), this pair is indeed a solution.
Based on the evaluations, the ordered pair that is part of the solution set for the equation \( y = 2.5x - 2 \) is:
**Option #3: (2, 3)**.
**Option #1: (−2,0)**
- Substitute \( x = -2 \):
\[
y = 2.5(-2) - 2 = -5 - 2 = -7
\]
The ordered pair is (−2, 0), and since \( 0 \neq -7 \), this pair is not a solution.
**Option #2: (2,5)**
- Substitute \( x = 2 \):
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is (2, 5), and since \( 5 \neq 3 \), this pair is not a solution.
**Option #3: (2,3)**
- Substitute \( x = 2 \):
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is (2, 3), and since \( 3 = 3 \), this pair is indeed a solution.
Based on the evaluations, the ordered pair that is part of the solution set for the equation \( y = 2.5x - 2 \) is:
**Option #3: (2, 3)**.