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!