Question
Use 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. The line passes through (0, 2) and (2, 3)
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)
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. The line passes through (0, 2) and (2, 3)
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 of the ordered pairs is part of the solution set for the equation \( y = 2.5x - 2 \), we can substitute each option into the equation and see which one satisfies it.
1. For Option #1: \( (-2, 0) \)
\[
y = 2.5(-2) - 2 = -5 - 2 = -7 \quad (\text{not } 0)
\]
This does not satisfy the equation.
2. For Option #2: \( (2, 5) \)
\[
y = 2.5(2) - 2 = 5 - 2 = 3 \quad (\text{not } 5)
\]
This does not satisfy the equation.
3. For Option #3: \( (2, 3) \)
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
This satisfies the equation.
Therefore, the correct answer is **Option #3: (2, 3)**.
1. For Option #1: \( (-2, 0) \)
\[
y = 2.5(-2) - 2 = -5 - 2 = -7 \quad (\text{not } 0)
\]
This does not satisfy the equation.
2. For Option #2: \( (2, 5) \)
\[
y = 2.5(2) - 2 = 5 - 2 = 3 \quad (\text{not } 5)
\]
This does not satisfy the equation.
3. For Option #3: \( (2, 3) \)
\[
y = 2.5(2) - 2 = 5 - 2 = 3
\]
This satisfies the equation.
Therefore, the correct answer is **Option #3: (2, 3)**.