Given the table for x, time in minutes and y, distance traveled:

Let's analyze the problem step by step based on the given data about time (x) and distance (y).

Based on the points you provided:

1. **Calculating the relationship between x (time) and y (distance):**
- To find how many meters are traveled per minute, we can calculate the slope (rate of change) using any two points.

- If we take two points from the table, let's say (4, 76) and (3, 57):
\[
\text{slope} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{57 - 76}{3 - 4} = \frac{-19}{-1} = 19
\]
This means that every minute, 19 meters are traveled.

**Answer a:** Every minute **19** meters are traveled.

2. **Writing the equation to show the relationship between x and y:**
- Since we have determined that the rate is 19 meters per minute, we can express this linear relationship as:
\[
y = 19x
\]
This means the distance is equal to 19 times the time in minutes.

**Answer b:** Write an equation to show the relationship between x and y: **y = 19x**.

3. **Identifying the nature of the relationship:**
- Since the relationship can be expressed as \(y = 19x\), it shows that there is a direct linear relationship through the origin (0,0).
- The y-intercept in this case is 0, confirming that when there is no time, there is no distance traveled.

**Answer c:** This relationship is **proportional** because the y-intercept is **(0, 0)**.

So, putting it all together:

a. Every minute **19** meters are traveled.
b. Write an equation to show the relationship between x and y: **y = 19x**.
c. This relationship is **proportional** because the y-intercept is **(0, 0)**.