Chapter 3, Problem 15CT

(a)

To determine

To find: the slope and the $y$ -intercept of the graph.

Answer to Problem 15CT

The slope of the function is $125$ and the $y$ -intercept is $50$ .

Explanation of Solution

Given:

  

Concept used:

The slope of the straight-line equation is denoted by $m$ and equation is in the form of:

  $y=mx+c$ .

Here $m$ is slope and $c$ is $y$ -intercept.

Calculation:

The function is $f\left(x\right)=125x+50$ .

The graph is:

  

Hence, the slope of the function is $125$ and the $y$ -intercept is $50$ .

(b)

To determine

To find: two ways to find $f\left(3\right)$ and interpret its meaning.

Answer to Problem 15CT

The slope is $375$ and $y$ - intercept is $50$ .

Explanation of Solution

Given:

  

Concept used:

The slope of the straight-line equation is denoted by $m$ and equation is in the form of:

  $y=mx+c$ .

Here $m$ is slope and $c$ is $y$ -intercept.

Slope of straight line is also can be calculated as:

  $m=\frac{y_2-y_1}{x_2-x_1}$ .

Calculation:

The graph of $f\left(3x\right)$ :

  

First method to find the slope of $f\left(3x\right)$ :

  $\begin{array}{l}f\left(x\right)=125x+50.\\ f\left(3x\right)=125\left(3x\right)+50.\\ f\left(3x\right)=375x+50.\end{array}$

Second method:

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}.\\ \Rightarrow \frac{0-50}{-0.133-0}.\\ \Rightarrow 375.\end{array}$

Hence, the slope is $375$ and $y$ - intercept is $50$ .

(c)

To determine

To find: the duration for the climber to reach the top of the cliff.

Answer to Problem 15CT

it took $3.6$ hours.

Explanation of Solution

Given:

  

Concept used:

The slope of the straight-line equation is denoted by $m$ and equation is in the form of:

  $y=mx+c$ .

Here $m$ is slope and $c$ is $y$ -intercept.

Where $x$ her is duration to climb the cliff.

Calculation:

The function is $y=375x+50,x=3.6$ hours the it takes the climber to reach the top of the cliff.

Hence, it took $3.6$ hours.