Question

On a coordinate plane, the x-axis is labeled minutes and the y-axis is labeled Blocks. Line A goes through points (10, 4), (15, 12), and (20, 20). Line B goes through points (5, 8), (10, 16), (15, 24). Line C goes through points (5, 24), (15, 16), (20, 12).
The table shows Jose’s rate of bicycle riding.

A 2-column table with 3 rows. Column 1 is labeled Minutes with entries 5, 10, 15. Column 2 is labeled Blocks with entries 8, 16, 24.

Which line on the graph shows the proportional relationship in the table?

Line
on the graph shows the proportional relationship.

Answer 1

To determine which line on the graph shows the proportional relationship in the table, we need to check if Jose's rate of bicycle riding is constant.

The table shows:

- At 5 minutes, Jose rides 8 blocks.
- At 10 minutes, he rides 16 blocks.
- At 15 minutes, he rides 24 blocks.

To check for proportionality, we can find the unit rate (blocks per minute):

1. From 5 to 10 minutes:
\[
\frac{16 - 8}{10 - 5} = \frac{8}{5} = 1.6 \text{ blocks/minute}
\]

2. From 10 to 15 minutes:
\[
\frac{24 - 16}{15 - 10} = \frac{8}{5} = 1.6 \text{ blocks/minute}
\]

3. From 5 to 15 minutes:
\[
\frac{24 - 8}{15 - 5} = \frac{16}{10} = 1.6 \text{ blocks/minute}
\]

Since the rate is constant and equals 1.6 blocks per minute, we can see that this is a proportional relationship.

Now, let's analyze the lines provided:

- Line A goes through points (10, 4), (15, 12), and (20, 20).
- Line B goes through points (5, 8), (10, 16), (15, 24).
- Line C goes through points (5, 24), (15, 16), (20, 12).

Looking at Line B:

- It contains the points (5, 8) at 5 minutes, (10, 16) at 10 minutes, and (15, 24) at 15 minutes, which match the values in the table correctly with a consistent rate of change.

Thus, the line that shows the proportional relationship in the table is:

**Line B.**