linear equations and applications

1. The following table shows the number of hours five car salespeople worked and the number of cars they sold. Using Excel, plot each point on the same graph where the first coordinate is the number of hours and the second coordinate is the number of cars sold (hours, cars). After plotting each point, explain if there is a linear relationship between the number of hours worked and the number of cars sold.

Sales Hours Worked Cars
Sold
Tim 40 3
Bob 26 5
Brandi 10 1
Kurt 60 1
Kelly 30 7

Graph:

Explanation of linear relationship:

2. Graph the following equations.

A.

Graph:

B.

Graph:

3. Answer the following questions pertaining to the following graph.

A. Give a brief explanation describing the graph in terms of its x-axis and y-axis.

B. In what year was the number of sales the highest?

C. Find the slope of the line. Show all work to receive full credit.

D. Write a sentence that explains the meaning of the slope within the context of this problem.

E. Find the equation of the line that represents the number of book sales. Show all work
to receive full credit.

F. Interpret the y-intercept of this equation.

4. For a 2-day rental, a rental car agency charges a $40 fee per day plus $0.35 per mile.
The equation represents this model, where C symbolizes the total cost of
the rental, and x stands for the number of miles driven.

A. Find the y-intercept of this graph and explain what it means in the context of the problem. Show all work to receive full credit.

B. Explain the slope of the line within the context of this problem.

C. Graph the equation.

5. The director of a summer day camp estimates that 120 children will join if the camp
fee is $250, but for each $25 decrease in the fee, five more children will enroll.

A. Determine the linear equation that will represent the number of children who will enroll at a given fee. Hint: To write the slope, you need two points on the line. Show all work to receive full credit.

B. Graph the linear equation that represents the number of children who will enroll at a given fee.

C. Approximately how many students will enroll if the camp fee is $190? Round to the nearest child. Show all work to receive full credit.

D. Approximately how many students will enroll if the camp is free? Round to the nearest child. Show all work to receive full credit.