Question

2. 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. Response area

c. This relationship is Response area because the y-intercept is Response area .

Answer 1

To analyze the data provided, we can look for patterns and create a linear equation based on those observations.

### Given Data:
- **Time (x)**: 4, 3, 10, 7, 9 (minutes)
- **Distance (y)**: 76, 57, 190, 133, 171 (meters)

### a. Every minute, ___ meters are traveled.
To find the average distance traveled per minute, we can calculate the slope (rate of change).

1. Calculate a few slopes between the data points:
- From (4, 76) to (3, 57):
\[
\text{slope} = \frac{57 - 76}{3 - 4} = \frac{-19}{-1} = 19 \text{ meters per minute}
\]
- From (3, 57) to (10, 190):
\[
\text{slope} = \frac{190 - 57}{10 - 3} = \frac{133}{7} \approx 19 \text{ meters per minute}
\]
- It appears the distance traveled per minute is consistently around 19 meters, so we can conclude:

*Every minute, 19 meters are traveled.*

### b. Write an equation to show the relationship between x and y.
We can use the slope-intercept form of a linear equation y = mx + b, where m is the slope and b is the y-intercept.

Using the slope we calculated (approximately 19 meters per minute), we can also choose one point to find the y-intercept. Let's use the point (4, 76):

\[
76 = 19(4) + b \Rightarrow 76 = 76 + b \Rightarrow b = 0
\]

So, the equation is:
\[
y = 19x + 0 \quad \text{or simply} \quad y = 19x
\]

### c. This relationship is ______ because the y-intercept is ______.
The relationship is **linear** because it can be expressed in the form of a linear equation, and the y-intercept is **0** (since the equation simplifies to y = 19x).

### Summary of the 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 **linear** because the y-intercept is **0**.