Question

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

x - time 4 3 10 7 9
y - distance 76 57 190 133 171


(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
a. Every minute ______ meters are traveled.
b. Write an equation to show the relationship between x and y. _____
c. This relationship is _____ because the y-intercept is _______
Answers: y=x/19. y=x-19n. y=133x. 19. 19y=x. (0,57). 57. y=19x. 76. (0,19). (4, 76). 133. proportional. -19. (0,0) non proportional

Answer 1

Let's break down the problem step by step using the provided information.

### Analyzing the relationship between x and y
1. First, let's identify the distance traveled per minute by finding the ratio of distance to time for any of the points in the table.
2. For example, if we take the first data point where x = 4 and y = 76:
- Distance per minute = 76 meters / 4 minutes = 19 meters per minute.
3. This ratio will hold for the other data points as well:
- 57 meters / 3 minutes = 19 meters per minute,
- 190 meters / 10 minutes = 19 meters per minute,
- 133 meters / 7 minutes = 19 meters per minute,
- 171 meters / 9 minutes = 19 meters per minute.

### Responses
Given this analysis, we can fill in the inputs:

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

b. To find the equation that shows the relationship between x (time in minutes) and y (distance in meters), since we've established that the relationship is linear and based on the ratio found above:
- The equation can be derived as \( y = 19x \).

Therefore, the response is:
- **y=19x.**

c. Since the relationship is linear and passes through the origin (0,0) and has a constant rate of change (19) with a y-intercept at y = 0, we conclude that:
- This relationship is **proportional** because the y-intercept is **(0,0)**.

### Full Responses
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)**.