Understanding Slope and Graphing Linear Costs

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write an equation to represent the total cost (C) in terms of miles driven (m). What is the slope of this equation?

• 0.20

• $0.10

• $1.00

• $0.50

If the equation from the previous problem is graphed, what does the slope represent in the context of the car rental?

• The slope represents the daily rental rate.

• The slope reflects the fuel efficiency of the car.

• The slope shows the number of cars available for rent.

• The slope indicates the total distance traveled.

A local gym charges a monthly membership fee of $30 plus $10 for each fitness class attended. Write the equation for the total cost (C) based on the number of classes (c) attended. What is the slope?

• The slope is 15.

• The slope is 5.

• The slope is 10.

• The slope is 30.

Using the equation from the previous problem, graph the total cost for attending 0 to 5 classes. What do the points on the graph represent?

• The points on the graph represent the total cost of attending a specific number of classes, showing how the cost increases with each additional class.

• The points on the graph represent the average cost per class.

• The points on the graph represent the number of classes attended.

• The points on the graph represent the total number of students attending classes.

A phone company offers a plan that costs $25 per month plus $0.05 per text message sent. Write the equation for the total cost (C) based on the number of text messages (t) sent. Identify the slope.

• C = 0.05 + 25t; slope = 25

• C = 25 + 0.05t; slope = 0.05

• C = 25t + 0.05; slope = 25

• C = 25 + 0.10t; slope = 0.10

If you were to graph the equation from the previous problem, what would the y-intercept represent in this scenario?

• The y-intercept indicates the slope of the graph.

• The y-intercept represents the rate of change in the scenario.

• The y-intercept represents the initial value of the dependent variable.

• The y-intercept shows the maximum value of the dependent variable.

A school is selling tickets for a play at $10 each. If they sell 50 tickets, they will also receive a $200 donation. Write an equation for the total revenue (R) based on the number of tickets sold (n). What is the slope?

• R = 10n; slope = 0

• R = 5n + 200; slope = 5

• R = 15n + 100; slope = 15

• R = 10n + 200; slope = 10

Graph the equation from the previous problem for ticket sales from 0 to 100. What does the graph tell you about the relationship between ticket sales and revenue?

• The graph suggests that ticket sales decrease as revenue increases.

• The graph shows no correlation between ticket sales and revenue.

• The graph indicates that lower ticket sales lead to higher revenue.

• The graph indicates a positive relationship between ticket sales and revenue, showing that higher ticket sales generally lead to higher revenue.

A delivery service charges a base fee of $15 plus $2 for each mile driven. Write the equation for the total charge (C) based on miles driven (d). What is the slope?

• The slope is 5.

• The slope is 15.

• The slope is 0.

• The slope is 2.

Using the equation from the previous problem, if you graph the total charge for distances from 0 to 10 miles, what does the slope indicate about the cost per mile?

• The slope represents the total distance traveled.

• The slope shows the average speed of travel.

• The slope indicates the total charge for the trip.

• The slope indicates the cost per mile.