Question

This table shows data collected by a runner.

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

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

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)

 $\frac{2-1}{26-12}\neq \frac{3-2}{67-26}\neq \frac{4-3}{98-67}$  

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

Answer:

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

Step-by-step 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.