Question

1. the table below shows the total miles run by forrest based on the number of hours he has been running.

number of hours x	total distance y
2.5	12.5
3	15
6	30

he made the following statements, shown below, about his run.

i. my data represents a linear relationship.
ii. the k - value in this situation is 5.
iii. the unit rate for this situation is \\(\frac{1}{5}\\).
iv. my data represents a proportional relationship.

which of his statements are true?

a. statements ii, iii, and iv
b. statements ii and iv only
c. statements i, ii, and iv
d. statements i, iii, and iv

Explanation:

Step1: Check Linear Relationship

To check if it's linear, calculate the slope between points. For (2,10) and (2.5,12.5): slope $m=\frac{12.5 - 10}{2.5 - 2}=\frac{2.5}{0.5}=5$. Between (2.5,12.5) and (3,15): $m=\frac{15 - 12.5}{3 - 2.5}=\frac{2.5}{0.5}=5$. Between (3,15) and (6,30): $m=\frac{30 - 15}{6 - 3}=\frac{15}{3}=5$. Constant slope, so linear (Statement I true).

Step2: Check k - value (Proportionality)

For proportional relationship, $y = kx$. From (2,10), $k=\frac{y}{x}=\frac{10}{2}=5$. Check others: $\frac{12.5}{2.5}=5$, $\frac{15}{3}=5$, $\frac{30}{6}=5$. So k = 5 (Statement II true), and proportional (Statement IV true).

Step3: Check Unit Rate

Unit rate (slope) is 5, not $\frac{1}{5}$ (Statement III false).

Answer:

C. Statements I, II, and IV