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se the image to answer the question. A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of...Question
se the image to answer the question.
A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. A line passes through the first, third, and fourth quadrants.
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)
(1 point)
Option #
is part of the solution set for the equation.
A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. A line passes through the first, third, and fourth quadrants.
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)
(1 point)
Option #
is part of the solution set for the equation.
Answers
GPT-4o mini
To determine which ordered pair is part of the solution set for the equation \( y = 2.5x - 2 \), we need to substitute the x-value from each option into the equation and see if the resulting y-value matches the y-value given in the ordered pair.
1. **Option #1: \( (-2, 0) \)**
\[
y = 2.5(-2) - 2 = -5 - 2 = -7
\]
The ordered pair is \( (-2, 0) \), but the calculated y-value is \(-7\). So this option is **not a solution**.
2. **Option #2: \( (2, 5) \)**
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is \( (2, 5) \), but the calculated y-value is \(3\). So this option is **not a solution**.
3. **Option #3: \( (2, 3) \)**
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is \( (2, 3) \), and the calculated y-value is \(3\). This matches, so this option **is a solution**.
So the answer is **Option #3: \( (2, 3) \)** is part of the solution set for the equation \( y = 2.5x - 2 \).
1. **Option #1: \( (-2, 0) \)**
\[
y = 2.5(-2) - 2 = -5 - 2 = -7
\]
The ordered pair is \( (-2, 0) \), but the calculated y-value is \(-7\). So this option is **not a solution**.
2. **Option #2: \( (2, 5) \)**
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is \( (2, 5) \), but the calculated y-value is \(3\). So this option is **not a solution**.
3. **Option #3: \( (2, 3) \)**
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
The ordered pair is \( (2, 3) \), and the calculated y-value is \(3\). This matches, so this option **is a solution**.
So the answer is **Option #3: \( (2, 3) \)** is part of the solution set for the equation \( y = 2.5x - 2 \).