Chapter 8.8, Problem 38PPS

(a)

To determine

Write an equation in slope − intercept form to represent the data.

Answer to Problem 38PPS

The equation in slope − intercept form to represent the data, is

  $y=40x+30$ .

Explanation of Solution

Given:

After two hours, repair bill is $\$110.$

After three hours, repair bill is $\$150.$ .

Slope − intercept form is $y=mx+c$

  $\left(2,110\right)\Rightarrow 110=m\left(2\right)+c\Rightarrow 2m+c=110$..........(1)

  $\left(3,150\right)\Rightarrow 150=m\left(3\right)+c\Rightarrow 3m+c=150$..........(2)

  $3m+c-2m-c=150-110$

  $m=40$

Put $m=40$ in eq. (1)

  $\begin{array}{l}\Rightarrow 2\left(40\right)+c=110\\ c=110-80\\ c=30\end{array}$

  $\therefore$ Equation in slope intercept from is

  $y=40x+30$

Conclusion:

Thus, the equation in slope − intercept form to represent the data, is

  $y=40x+30$ .

(b)

To determine

Describe the solution the slope and $y$ -intercept

Answer to Problem 38PPS

The solution the slope and $y$ -intercept $\left(c\right)=30$ .

Explanation of Solution

Given:

After two hours, repair bill is $\$110.$

After three hours, repair bill is $\$150.$ .

Slope − intercept form is $y=mx+c$

There slope $\left(m\right)=40$ is hourly charge and $y$ - intercept $\left(c\right)=30$ is free charged.

Conclusion:

The solution the slope and $y$ -intercept $\left(c\right)=30$ .

(c)

To determine

The cost for the 1.5 hours of work.

Answer to Problem 38PPS

The cost for the 1.5 hours of workis $\$90$ .

Explanation of Solution

Given:

After two hours, repair bill is $\$110.$

After three hours, repair bill is $\$150.$ .

Slope − intercept form is $y=mx+c$

Finding the cost for $1.5$ hrs of work

  $\begin{array}{l}y=mx+c\\ m=40;x=1.5;c=30\\ y=\left(40\right)\left(1.5\right)+30\\ y=90\end{array}$

  $\therefore$ It costs $\$90$ for $1.5$ hrs of work.

Conclusion:

The cost for the 1.5 hours of workis $\$90$ .