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. 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 Response area meters are traveled. b. Write an equation to show the relationship between x and y. Response area c. The relationship is Response area because the y-intercept is Response area

Answer 1

To address the given questions based on the provided data, we can start by analyzing the relationship between time (x) and distance (y).

**a. Every minute**
To determine the distance traveled per minute, we can calculate the average distance traveled per minute based on the given data:

- Total distance traveled (sum of y): \(40 + 25 + 35 + 10 + 45 = 155\) meters.
- Total time (sum of x): \(8 + 5 + 7 + 2 + 9 = 31\) minutes.

Average distance per minute = Total distance / Total time = \(155 \, \text{meters} / 31 \, \text{minutes} \approx 5 \, \text{meters}\).

**Response:** 5

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**b. Write an equation to show the relationship between x and y.**
To find the equation relating x and y, we can analyze the pairs given:

Using the slope formula \( m = \frac{\Delta y}{\Delta x} \):
- For specific pairs, we can choose (2, 10) and (9, 45):
\[
m = \frac{45 - 10}{9 - 2} = \frac{35}{7} = 5 \text{ meters per minute.}
\]
The equation of the line in slope-intercept form is \(y = mx + b\). Here \(m = 5\).

Now we have to find \(b\) (the y-intercept). We can use a point; for (2, 10):
\[
10 = 5(2) + b \implies 10 = 10 + b \implies b = 0.
\]

**Response:** \(y = 5x\)

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**c. The relationship is**
The relationship we have is a linear relationship, as represented by the equation we derived.

**Response:** linear

**because the y-intercept is**
The y-intercept we found is 0.

**Response:** 0

So the final completed inputs would be:
- a: **5**
- b: **y = 5x**
- c: **linear**
- because the y-intercept is: **0**