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

Answer 1

To analyze the table you've provided, we'll start with the given data:

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

### a. Every minute meters are traveled.

To find the average distance traveled per minute, we can calculate the rate of distance traveled per minute.

1. First, we'll calculate the total distance traveled and the total time taken.

- Total distance traveled (y):
\( 664 + 415 + 581 + 166 + 747 = 2573 \) meters

- Total time (x):
\( 8 + 5 + 7 + 2 + 9 = 31 \) minutes

2. Calculate the average distance per minute:

\[
\text{Average distance per minute} = \frac{\text{Total distance}}{\text{Total time}} = \frac{2573}{31} \approx 83.3 \text{ meters per minute}
\]

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

Let’s assume a linear relationship \( y = mx + b\), where:

- **m** = slope (the average distance traveled per minute)
- **b** = y-intercept (the distance traveled when \( x = 0\))

Given our previous calculation, we can set up our equation using the average calculated slope.

Assuming there's no initial distance covered when time \( x = 0 \), we typically have \( b = 0 \) for simplification in this context. Thus, since the average distance is approximately 83.3:

\[
y = 83.3x + 0
\]

Or, simplifying:

\[
y = 83.3x
\]

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

The relationship is **linear** because it can be expressed in the form \( y = mx + b\). The y-intercept is **0**, indicating that when no time has passed (0 minutes), no distance has been traveled (0 meters).

So, filling in the blanks:

- This relationship is **linear** because the y-intercept is **0**.