Question

Hours/miles walked: (1,2); (2,4); (3,6); (4,8); (5,10), Use the graph to fill in the blanks. (The constant of the proportionality is (1,2); Write an equation that represents this graph (y = 2x); This is a proportional relationship because the y - intercept is (2)

Answer 1

It looks like there are some inaccuracies in the statements you provided about the proportional relationship. Let's clarify each point:

1. **Hours/Miles Walked Data**: The pairs you've provided represent a proportional relationship where the second number is always twice the first number. Specifically:
- (1, 2)
- (2, 4)
- (3, 6)
- (4, 8)
- (5, 10)

2. **Constant of Proportionality**: The constant of proportionality can be found by dividing the second value by the first value. In this case, \( k = \frac{y}{x} = \frac{2}{1} = 2 \). This constant applies to all pairs, so the correct constant of proportionality here is **2**.

3. **Equation**: The equation representing the relationship between hours \( x \) and miles \( y \) can be written as:
\[
y = 2x
\]
This means that for every hour walked, 2 miles are covered.

4. **Proportional Relationship**: This is indeed a proportional relationship, but the y-intercept should be noted as **0**, not **2**. In a proportional relationship, the line passes through the origin (0, 0), meaning when \( x = 0 \), \( y = 0 \).

Here's the corrected summary:

- **Constant of proportionality**: 2
- **Equation that represents this graph**: \( y = 2x \)
- **This is a proportional relationship because the y-intercept is (0)**.

Feel free to ask if you need further clarification or have more questions!