Which of the following ordered pairs is part of the solution set for the equation 
y=2.5x−2
y=2.5x−2?
Option #1: 
(−2,0)
(−2,0)
Option #2: 
(2,5)
(2,5)
Option #3: 
(2,3



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.**

---

### 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.**

---

### 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.

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

Learn how to determine which ordered pairs satisfy the linear equation y = 2.5x - 2 by substituting values. This problem involves testing multiple options and understanding the substitution method. Suitable for students in Grades 7-9.

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