Chapter 8.7, Problem 24PPS

(a)

To determine

To calculate: To graph the equation

Answer to Problem 24PPS

Graph of equation is plotted.

Explanation of Solution

Given information: To replace a set of brakes, an auto mechanic charges $\$40$ for parts plus $\$50$ per hour. The total cost $y$ can be given as $y=50x+40$ for $x$ hours

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Equation is given as

  $y=50x+40$

Comparing the above equation to slope intercept form of line $y=mx+c$ , slope and Y-intercept are

  $\begin{array}{l}m=50\\ c=40\end{array}$

Thus, y-intercept is at $\left(0,40\right)$ , which is the first point

Also, $m=50$ , this means that one will rise 50 (up) and run 1(to the right)

Thus, other point is $\left(1,90\right)$

On plotting the graph,

  

(b)

To determine

To calculate: To state slope and y-intercept of the graph of the equation and describe what they represent

Answer to Problem 24PPS

Slope is $50$ and y-intercept is $40$

Explanation of Solution

Given information: To replace a set of brakes, an auto mechanic charges $\$40$ for parts plus $\$50$ per hour. The total cost $y$ can be given as $y=50x+40$ for $x$ hours

Formula Used:

Slope intercept form of line is $y=mx+c$ , where

  $m=$ Slope of graph of equation

  $c=$ y-intercept of graph of equation

Calculation:

Equation is given as

  $y=50x+40$

Comparing the above equation to slope intercept form of line $y=mx+c$ , slope and Y-intercept are

  $\begin{array}{l}m=50\\ c=40\end{array}$

Slope represents the cost of each hour.

Y-intercept represents the initial cost at hour $x=0$