A. input-output pairs of relationship. B.description of relationship( in words). C.mathematical model( equation)... relationship 1. A. 1-3, 2-5, 3-7, 4-9. B. blank. C y=2x+1

Let's break down the given relationship:

### A. Input-Output Pairs (Given):
- (1, 3)
- (2, 5)
- (3, 7)
- (4, 9)

### B. Description of Relationship (in words):
The output increases by 2 units for every 1-unit increase in the input. This indicates a **linear relationship** between the input and the output. Starting from an initial output of 3 when the input is 1, the output grows steadily. Specifically, the output is always 1 more than twice the input value.

### C. Mathematical Model (Equation):
The equation that models this relationship is already provided:
\[
y = 2x + 1
\]
where:
- \( y \) is the output,
- \( x \) is the input,
- 2 is the rate of change (slope), and
- 1 is the y-intercept, meaning that when \( x = 0 \), \( y = 1 \).

Would you like more details or explanations?

### Related Questions:
1. How would the relationship change if the equation were \( y = 2x - 1 \)?
2. Can you determine the output if the input is 5 using this equation?
3. What does the slope \( 2 \) represent in practical terms for this relationship?
4. How would the graph of this linear relationship look?
5. How can you find the input given an output of 15?

### Tip:
When analyzing linear relationships, always pay attention to the slope and intercept in the equation, as they determine the rate of change and starting point, respectively.

Explore the linear relationship defined by the equation y = 2x + 1. Understand the input-output pairs (1, 3), (2, 5), (3, 7), and (4, 9) and how they correspond to this linear model. Ideal for students in Grades 6-8 studying basic algebra and linear equations.

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