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 of the ordered pairs is part of the solution set for the equation \( y = 2.5x - 2 \), we will substitute the x-values from each option into the equation and see if the corresponding y-values match.

Option #1: \((-2, 0)\)

Substituting \(-2\) for \(x\): \[ y = 2.5(-2) - 2 = -5 - 2 = -7 \] This gives the point \((-2, -7)\), which does not match \((-2, 0)\).

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

Substituting \(2\) for \(x\): \[ y = 2.5(2) - 2 = 5 - 2 = 3 \] This gives the point \((2, 3)\), which does not match \((2, 5)\).

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

Substituting \(2\) for \(x\): \[ y = 2.5(2) - 2 = 5 - 2 = 3 \] This indeed gives the point \((2, 3)\), which matches the option.

Thus, the ordered pair that is part of the solution set for the equation is:

Option #3: (2, 3).