Mastering Linear Functions: Real-World Applications Quiz

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear function to represent the total cost (C) based on the number of miles (m) driven. What is the slope of this function?

• $0.20 per hour

• 0.20

• $50

• 0.50

If you graph the function from the previous question, what would be the y-intercept? Explain its meaning in the context of the problem.

• The y-intercept is the slope of the function at x=0.

• The y-intercept is the value of the function at x=0.

• The y-intercept occurs where the function crosses the x-axis.

• The y-intercept is the maximum value of the function.

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

• C = 30 + 5c; slope = 5

• C = 20 + 10c; slope = 10

• C = 30 + 15c; slope = 15

• C = 30 + 10c; slope = 10

Using the equation from the previous question, graph the total cost for attending 0 to 10 classes. What does the graph look like?

• The graph is a zigzag line fluctuating between (0, 50) and (10, 150).

• The graph is a straight line with a slope, starting at (0, 50) and ending at (10, 150).

• The graph is a horizontal line at y = 100.

• The graph is a parabola starting at (0, 50) and ending at (10, 200).

A delivery service charges a base fee of $15 plus $2 for each mile delivered. If you were to graph this function, what would the equation look like?

• C = 15 - 2m

• C = 2m + 15

• C = 15 + 2m

• C = 15m + 2

If a customer wants to know the total cost for a delivery of 5 miles, how would you calculate it using the equation from the previous question?

• Total cost = Base fee + (5 miles * Per-mile rate)

• Total cost = Base fee - (5 miles * Per-mile rate)

• Total cost = Base fee + (10 miles * Per-mile rate)

• Total cost = Per-mile rate * 5 miles

A school is selling tickets for a play at $8 each. If they sell 50 tickets, how much money will they make? Write a linear function to represent the total revenue (R) based on the number of tickets (t) sold. What is the slope?

• The total revenue is $200, and the slope is 4.

• The total revenue is $400, and the slope is 8.

• The total revenue is $300, and the slope is 6.

• The total revenue is $500, and the slope is 10.

Graph the revenue function from the previous question for ticket sales from 0 to 100. What does the graph indicate about revenue as ticket sales increase?

• The graph indicates that revenue remains constant regardless of ticket sales.

• The graph indicates that revenue generally increases as ticket sales increase.

• The graph suggests that revenue is unrelated to ticket sales.

• The graph shows that revenue decreases as ticket sales increase.

A phone company offers a plan that costs $25 per month plus $0.10 per text message sent. Write the linear equation for the total cost (C) based on the number of text messages (t) sent. What does the y-intercept represent?

• C = 25 + 0.10t; y-intercept represents the fixed monthly cost of $25.

• C = 25t + 0.10; y-intercept represents the total cost for unlimited texts.

• C = 0.10t; y-intercept represents the cost per text message.

• C = 25 + 0.05t; y-intercept represents the monthly cost with a discount.

Using the equation from the previous question, if a customer sends 200 text messages, what will their total cost be? Show your calculations.

• $25.00

• $20.00

• $15.00

• $30.00