To determine which ordered pair is part of the solution set for the equation $y = 2.5x - 2$, we substitute the $x$ and $y$ values from each pair into the equation and check if the equation holds true.

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

Substitute $x = -2$ and $y = 0$ into the equation $y = 2.5x - 2$:
$0 = 2.5(-2) - 2$ $0 = -5 - 2$ $0 = -7 \quad \text{(False)}$
This pair is not a solution.

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Option #2: $(2, 5)$

Substitute $x = 2$ and $y = 5$ into the equation $y = 2.5x - 2$:
$5 = 2.5(2) - 2$ $5 = 5 - 2$ $5 = 3 \quad \text{(False)}$
This pair is not a solution.

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Option #3: $(2, 3)$

Substitute $x = 2$ and $y = 3$ into the equation $y = 2.5x - 2$:
$3 = 2.5(2) - 2$ $3 = 5 - 2$ $3 = 3 \quad \text{(True)}$
This pair is a solution.

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Final Answer:

The ordered pair $(2, 3)$ is part of the solution set.

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Would you like further details on verifying solutions or graphing linear equations?

Related Questions:

1. How do you find solutions for equations in two variables?
2. What does the slope in $y = 2.5x - 2$ represent?
3. Can we graph $y = 2.5x - 2$ to verify these points visually?
4. What are other examples of ordered pairs that satisfy $y = 2.5x - 2$?
5. How can equations like $y = 2.5x - 2$ model real-world scenarios?

Tip:

For any equation, an ordered pair is a solution only if it satisfies the equation when the values of $x$ and $y$ are substituted.