Chapter 9.5, Problem 24IP

a.

To determine

To graph the equation using slope and y-intercept.

Explanation of Solution

Given information:

The given statement is:

“To replace a set of brakes, an auto mechanics charges $\$40$ for parts plus $\$50$ per hour. The total cost $\text{y}$ can be given by $\text{y}=50\text{x}+40$ for $\text{x}$ hours.”

Graph:

The slope of the equation is $50$ and the y-intercept is $40$ .

Graph the y-intercept at $\left(0,40\right)$ .

Using the slope $50$ locate another point on the line.

Move $\text{y}$ up by $\text{50 units}$ and move $\text{x}$ right by $1\text{ unit}$ .

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

Draw a line through the two points.

The graph is:

  

b.

To determine

To state and describe what the slope and y-intercept represents.

Answer to Problem 24IP

The y-intercept $40$ represents the money charged by the mechanic for parts.

The slope of the equation $50$ represents the rate of money charged by the mechanic per hour.

Explanation of Solution

Given information:

The given statement is:

“To replace a set of brakes, an auto mechanics charges $\$40$ for parts plus $\$50$ per hour. The total cost $\text{y}$ can be given by $\text{y}=50\text{x}+40$ for $\text{x}$ hours.”

The y-intercept $40$ represents the money charged by the mechanic for parts.

The slope of the equation $50$ represents the rate of money charged by the mechanic per hour.