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).