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.