Question

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

x: time 8 5 7 2 9
y: distance 664 415 581 166 747


(4 points)
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

-12
83
656
y=83x
y = x - 83
12y =x
y = 12x
proportional
non proportional
(0,0)
(8,664)
(0,83)

Answer 1

To analyze the relationship between time (x) and distance traveled (y) based on the provided data, we'll go through each part of the question step by step.

### Given data:
- x (time in minutes): 8, 5, 7, 2, 9
- y (distance traveled in meters): 664, 415, 581, 166, 747

### a. Every minute ____ meters are traveled.

To find the average meters traveled per minute, we can calculate the ratio of distance to time for each pair and then find the average:

1. For (8, 664): \( \frac{664}{8} = 83\)
2. For (5, 415): \( \frac{415}{5} = 83\)
3. For (7, 581): \( \frac{581}{7} \approx 83\) (exactly 83.86, but we take the average)
4. For (2, 166): \( \frac{166}{2} = 83\)
5. For (9, 747): \( \frac{747}{9} \approx 83\) (exactly 83, as it's 83.0)

This suggests that every minute approximately **83 meters** are traveled.

### b. Write an equation to show the relationship between x and y:

Since we determined the average meters per minute is 83, we can express the relationship (assuming this is linear) as:

\( y = 83x \)

### c. This relationship is ____ because the y-intercept is ____.

Now, let's determine if the relationship is proportional or non-proportional:
- A linear relationship of the form \(y = mx + b\) is proportional if \(b = 0\) (the y-intercept is 0). If there is a non-zero y-intercept (b ≠ 0), it is non-proportional.

In our case, \( y = 83x \) has a y-intercept of \(0\) (which means when \(x = 0, y = 0\)), indicating a proportional relationship.

Therefore, the answers are as follows:

- a. Every minute **83** meters are traveled.
- b. Write an equation: \( y = 83x \)
- c. This relationship is **proportional** because the y-intercept is **(0,0)**.

So the completed answers are:
a. **83**
b. **y = 83x**
c. **proportional**; y-intercept is **(0,0)**.