To determine the proportional relationship represented by the table, let's analyze the data points you've provided:
- When Jose rides for 5 minutes, he covers 8 blocks.
- When he rides for 10 minutes, he covers 16 blocks.
- When he rides for 15 minutes, he covers 24 blocks.
To see if this relationship is proportional, we can calculate the rate (blocks per minute) for each point:
-
For 5 minutes:
\[ \text{Rate} = \frac{8 \text{ blocks}}{5 \text{ minutes}} = 1.6 \text{ blocks per minute} \] -
For 10 minutes:
\[ \text{Rate} = \frac{16 \text{ blocks}}{10 \text{ minutes}} = 1.6 \text{ blocks per minute} \] -
For 15 minutes:
\[ \text{Rate} = \frac{24 \text{ blocks}}{15 \text{ minutes}} = 1.6 \text{ blocks per minute} \]
Since the rate remains constant at 1.6 blocks per minute, this indicates that the relationship is indeed proportional.
To represent this on a graph, you would plot each point (5, 8), (10, 16), and (15, 24) and draw a straight line through them, showing the consistent rate of 1.6 blocks per minute. When graphed, the line will pass through the origin (0,0), confirming the proportional relationship.
If you are looking for the equation of this relationship, it can be expressed as:
\[ y = 1.6x \]
where \(y\) is the number of blocks, and \(x\) is the time in minutes.