Question

This table shows data collected by a runner.

Which statement about the scenario represented in the table is true?

A. The distance run is a nonlinear function because it does not have a constant rate of change.
B. The elevation is a nonlinear function because it does not have a constant rate of change.
C. Both the distance run and the elevation are nonlinear functions because they do not have constant rates of change.
D. Both the distance run and the elevation are linear functions because they have a constant rate of change.

Answer 1

Answer with explanation:

Distance with time

1. If we plot time on y axis and Distance on x axis ,the set of points will be (0.19,1),(0.38,2),(0.57,3),(0.76,4),(0.95,5),(1.14,6).

Finding the slope between points

`(x_(1),y_(1)),(x_(2),y_(2)){\text{Using the formula}}\\\\m=(y_(2)-y_(1))/(x_(2)-x_(1))\\\\m=(2-1)/(0.38-0.19)=(3-2)/(0.57-0.38)=(4-3)/(0.76-0.57)=(5-4)/(0.95-0.76)=(6-5)/(1.14-0.95)=(6-1)/(1.14-0.19)=(1)/(0.19)`

Since the slope between any two points is same ,so the given function is linear.

Elevation with Time

2. If we plot time on y axis and Elevation on x axis ,the set of points will be, (12,1),(26,2),(67,3),(98,4),(124,5),(145,6)

`(2-1)/(26-12)\\eq (3-2)/(67-26)\\eq (4-3)/(98-67)`

Slope between two points is not same .So, this is not a linear function.

Option B: The elevation is a nonlinear function because it does not have a constant rate of change.

Answer 2

B. The elevation is a nonlinear function because it does not have a constant rate of change.

Explanation:

Looking at the distance run, we can see that between any two consecutive times, the distance increases by 0.19 miles. This occurs throughout the entire table; this tells us that distance is a linear function.

Looking at the elevation, we can see that between any two consecutive times, the elevation increases by varying amounts. This means elevation is a nonlinear function.