Question

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

x - time (minutes) 8 5 7 2 9
y - distance (meters) 40 25 35 10 45


(4 points)
Put responses in the correct input to answer the question.

a. Every minute [_] meters are traveled.

b. Write an equation to show the relationship between x and y. [_]

c. The relationship is [_] because the y-intercept is [_]

Answer 1

To find the answers to your questions, we can analyze the given data for time (x) and distance (y).

**Given values:**
- \(x\) (time in minutes): 8, 5, 7, 2, 9
- \(y\) (distance in meters): 40, 25, 35, 10, 45

### a. Every minute [_] meters are traveled.

To find the average rate of distance traveled per minute, we can calculate the total distance traveled and divide it by the total time taken.

Total distance:
\(40 + 25 + 35 + 10 + 45 = 155\) meters

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

Average rate:
\[
\text{Average rate} = \frac{\text{Total distance}}{\text{Total time}} = \frac{155}{31} \approx 5 \text{ meters per minute}
\]

So, we can fill in the blank:

**a. Every minute [5] meters are traveled.**

---

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

To find the relationship between time (x) and distance (y), let's assume a linear relationship of the form:

\[ y = mx + b \]

Where \(m\) is the slope (distance per minute) and \(b\) is the y-intercept.

From our calculation above, we found that the average distance per minute (slope \(m\)) is approximately 5. To find the y-intercept (\(b\)), we can choose a pair of data points; let's use the first point (8, 40).

Using the equation:
\[
y = mx + b
\]
We can plug in \(y = 40\), \(m = 5\), and \(x = 8\):

\[
40 = 5(8) + b \\
40 = 40 + b \\
b = 0
\]

Thus, the relationship can be expressed as:
\[
y = 5x + 0 \\
\text{or simply} \\
y = 5x
\]

So we fill in the blank:

**b. Write an equation to show the relationship between x and y. [y = 5x]**

---

### c. The relationship is [_] because the y-intercept is [_].

We have determined that the relationship is linear because we have established a linear equation in the format \(y = mx + b\) with a constant slope.

Since \(b\) (the y-intercept) is 0, we can fill in the blanks:

**c. The relationship is [linear] because the y-intercept is [0].**