Chapter 3, Problem 12CT

a.

To determine

To find: The slope and the y -intercept of the graph

Answer to Problem 12CT

Slope is 125 and y - intercept is 50.

Explanation of Solution

Given:

Equation of the graph $f(x)=125x+50$

Formula used: Slope, $m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Slope, $m=\frac{y_2-y_1}{x_2-x_1}$

  $x_1$=0 $x_2$ =3.6

  $y_1$ =50 $y_2$ =500

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{500-50}{3.6-0}$

  $m=125$

Also the equation of the graph $f(x)=125x+50$ , which is a straight line. Comparing it with $y=mx+c$ we get $m=125$ and $c=50$ , thus slope is 125 and y − intercept is 50.

Conclusion:

Slope is 125 and y − intercept is 50.

b.

To determine

To find: Two ways to find $f(3)$

Answer to Problem 12CT

The two ways to find $f(3)$ is by solving the equation by plugging $x=3$ and second is by graphically looking at the x and y coordinate.

Explanation of Solution

Given:

  $f(x)=125x+50$

Calculation:

Method 1:

Plug $x=3$ into $f(x)=125x+50$

That is,

  $\begin{array}{l}f(3)=125(3)+50\\ f(3)=425\end{array}$

Method 2:

Go to where $x=3$ on the graph and find where it land on the equation line. Now $f(3)=425$ means at 3hrs climber will be at 425ft.

Thus, the two ways to find $f(3)$ is by solving the equation by plugging $x=3$ and second is by graphically looking at the x and y coordinate.

c.

To determine

To find: The time taken to reach the top of the cliff.

Answer to Problem 12CT

It takes $3.6\text{hrs}$ to reach the top of the cliff.

Explanation of Solution

Given:

  $f(x)=125x+50$

Calculation:

The height of the cliff is 500 ft. Putting $f(x)=500$ in the equation $f(x)=125x+50$ , we will get

  $\begin{array}{c}f(x)=125x+50\\ 500=125x+50\\ 500-50=125x\\ 450=125x\\ x=\frac{450}{125}=3.6\end{array}$

Thus the time taken to reach the top of the cliff is 3.6 hrs.