https://file.aiquickdraw.com/mathbot/file/1726839952055fimwv3m5.jpg

The graph shows two functions, \( y = x + 2 \) (in red) and \( y = 2x + 1 \) (in blue), intersecting at the point \( (1,3) \). Let's evaluate the provided statements:

1. **The point of intersection means that when \( x = 1 \), the two functions will have the same value of \( y \), which is \( 3 \)**:
   - This statement is **true** because at the point of intersection \( (1,3) \), both functions have the same \( y \)-value of \( 3 \) when \( x = 1 \).

2. **The point of intersection means that when \( x = 3 \), the two functions will have the same value of \( y \), which is \( 1 \)**:
   - This statement is **false**. When \( x = 3 \), the value of \( y \) for each function differs:
     - For \( y = x + 2 \), \( y = 3 + 2 = 5 \).
     - For \( y = 2x + 1 \), \( y = 2(3) + 1 = 7 \).

3. **The point of intersection shows that the two functions are inverse**:
   - This statement is **false**. The two functions are not inverses of each other; their intersection simply shows that they have the same \( y \)-value at one point.

4. **The two functions are equivalent**:
   - This statement is **false**. The two functions are not equivalent; they represent two distinct lines with different slopes.

### Conclusion:
The correct statement is the first one: **The point of intersection means that when \( x = 1 \), the two functions will have the same value of \( y \), which is \( 3 \).**

Would you like more details or have any other questions?

### 5 Related Questions:
1. How do you find the point of intersection between two linear functions?
2. What does it mean when two lines intersect at a point?
3. Can two distinct linear functions be equivalent?
4. How do you verify if two functions are inverse to each other?
5. What is the significance of the slope in determining the nature of two lines?

### Tip:
For any two linear functions, the point of intersection can be found by solving their equations simultaneously (setting them equal and solving for \( x \) and \( y \)).

Based on the graph, which statement is true?

Understand how to determine the point of intersection between two linear functions, y = x + 2 and y = 2x + 1, through graph analysis. The correct answer shows that the two functions intersect at the point (1, 3), meaning both have the same y-value when x = 1.

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