Question

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 Response area 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 choices:)0,19),57,-19,y=x-19,y=x/19,76,y=133x,19y=x,y=19x,(4,76),133, non proportional,19,(0,57),(0,0), proportinal

Answer 1

Let's analyze the data provided in order to answer the questions:

1. The distance traveled (y) per minute (x) can be found by calculating the slope of the line formed by the data points.

To find the slope (rate of change of distance with respect to time), we need to calculate how much distance is traveled for each minute. We can do this using one of the data pairs:
- For example, (4, 76) to (3, 57):
\[
\text{slope} = \frac{76 - 57}{4 - 3} = \frac{19}{1} = 19
\]
This rate is consistent across all points.

Thus, the average rate of distance traveled is **19 meters per minute**.

**Responses:**
a. Every minute **19** meters are traveled.

2. Next, we need to find the equation showing the relationship between x and y. The general linear equation is given by:
\[
y = mx + b
\]

Here, \(m\) (the slope) is 19 and \(b\) (the y-intercept) can be calculated by substituting a point into the equation. Choosing (4, 76):
\[
76 = 19(4) + b \quad \Rightarrow \quad 76 = 76 + b \quad \Rightarrow \quad b = 0
\]

So, the relationship can be expressed as:
\[
y = 19x
\]

**Responses:**
b. Write an equation to show the relationship between x and y: **y=19x**.

3. Next, we need to determine if this relationship is proportional or non-proportional. Since the equation passes through the origin (0,0) and the y-intercept is **0**, we can conclude that this is a proportional relationship.

**Responses:**
c. This relationship is **proportional** because the y-intercept is **(0, 0)**.

### Final 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 **proportional** because the y-intercept is **(0, 0)**.