Chapter 8.4, Problem 17E

a.

To determine

To find:

The slope of the line.

Answer to Problem 17E

The slope of the line would be 27.

Explanation of Solution

Given:

The graph shows distance run by a Cheetah as a function of time.

  

Concept used:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1},\text{where,}\\ m=\text{Slope of line,}\\ y_2-y_1=\text{Difference between two }y\text{-coordinates}\\ x_2-x_1=\text{Difference between two }x\text{-coordinates of same }y-\text{coordinates}\end{array}$

Calculation:

We can see that points $(1,27)\text{and (2,54})$ lie on our given line. Let point $(1,27)=(x_1,y_1)\text{and (2,54})=(x_2,y_2)$ . Upon substituting our given coordinates in slope formula, we will get:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{54-27}{2-1}\\ m=\frac{27}{1}\\ m=27\end{array}$

Therefore, the slope of the line would be27.

b.

To determine

What information about the cheetah can you obtain from the slope?

Answer to Problem 17E

Cheetah runs 27 meters per second.

Explanation of Solution

Given:

The graph shows distance run by a Cheetah as a function of time.

  

Calculation:

We got in part (a) that the slope of the line is 27. The y -axis represents distance run by cheetah in meters and x -axis represents time in seconds.

So slope represents change in distance run by cheetah with change in time.

Therefore, the slope represents that speed of cheetah is 27 meters per second.

c.

To determine

Suppose you made a graph showing the distance run by a gazelle as a function of time. How would the graph for the gazelle compare with the graph of cheetah? Explain your thinking.

Answer to Problem 17E

The graph for the gazelle will be less steeper than graph for the cheetah.

Explanation of Solution

Given:

A gazelle’s top speed is about 22 meters per second.

Calculation:

We know that speed of cheetah is 27 meters per second.

Since gazelle’s top speed is about 22 meters per second, so slope for the gazelle’s graph is less than slope for cheetah’s graph.

Therefore, the graph for the gazelle will be less steeper than graph for the cheetah.