Which of the following ordered pairs is part of the solution set for the equation y=2.5x−2

Question

𝑦
=
2.5
𝑥
−
2
?

Option #1: (−2,0)
(
−
2
,
0
)


Option #2: (2,5)
(
2
,
5
)


Option #3: (2,3)
(
2
,
3
)


(1 point)
Option # is part of the solution set for the equation.

Answer 1

To determine which ordered pair is part of the solution set for the equation \( y = 2.5x - 2 \), we can substitute the \( x \) value of each pair into the equation and see if the resulting \( y \) value matches the \( y \) coordinate of the ordered pair.

1. Option #1: (−2, 0)
   Substitute \( x = -2 \): \[ y = 2.5(-2) - 2 = -5 - 2 = -7 \] Here, \( y = -7 \), but the ordered pair has \( y = 0 \). So, this pair is not a solution.

2. Option #2: (2, 5)
   Substitute \( x = 2 \): \[ y = 2.5(2) - 2 = 5 - 2 = 3 \] Here, \( y = 3 \), but the ordered pair has \( y = 5 \). So, this pair is not a solution.

3. Option #3: (2, 3)
   Substitute \( x = 2 \): \[ y = 2.5(2) - 2 = 5 - 2 = 3 \] Here, \( y = 3 \), which matches the ordered pair \( (2, 3) \). So, this pair is a solution.

Based on the calculations, the correct answer is:

Option #3 is part of the solution set for the equation \( y = 2.5x - 2 \).