Question

the graph shows the relationship between time and distance for masons training run.
a. does the graph show a proportional relationship? how do you know?
b. what is the unit rate for masons run?
c. what does the unit rate mean in this situation?

Explanation:

Step1: Check for proportionality

A proportional relationship has a straight - line graph passing through the origin (0,0). The given graph is a straight line and passes through the origin, so it shows a proportional relationship.

Step2: Calculate unit rate

The unit rate is the ratio of distance to time. From the graph, when time \(x = 4\) minutes, distance \(y=800\) meters. The unit rate \(r=\frac{y}{x}=\frac{800}{4}=200\) meters per minute.

Step3: Interpret unit rate

The unit rate of 200 meters per minute means that Mason runs 200 meters in 1 minute.

Answer:

a. Yes, the graph shows a proportional relationship because it is a straight - line graph passing through the origin.
b. The unit rate for Mason's run is 200 meters per minute.
c. The unit rate means Mason runs 200 meters in 1 minute.