Mastering Linear Equations: Graph Features & Word Problems

A car rental company charges a flat fee of $50 plus $20 for each day the car is rented. Write the equation that represents the total cost (C) as a function of the number of days (d) rented. What is the slope of the line, and what does it represent in this context?

• C = 50 + 30d; slope = 30

• C = 50 + 10d; slope = 10

• C = 20 + 50d; slope = 50

• C = 50 + 20d; slope = 20

A local gym has a membership fee of $30 and charges $10 per class attended. If you graph the total cost (C) as a function of the number of classes (c) attended, what is the y-intercept and what does it signify?

• 30

• 10

• 0

• 40

A school is selling tickets for a play. The tickets cost $8 each, and there is a one-time fee of $50 for the venue. Write the equation for the total revenue (R) as a function of the number of tickets sold (t). How would you interpret the slope of this equation?

• R(t) = 8t + 50

• R(t) = 50 + 8t^2

• R(t) = 50t + 8

• R(t) = 8t - 50

A delivery service charges a base fee of $15 plus $2 for each mile driven. If you graph the total charge (C) against the number of miles (m), what does the point (0, 15) represent?

• The total charge when 10 miles are driven.

• The total charge when 5 miles are driven.

• The base fee of the delivery service.

• The total charge when no miles are driven.

A farmer sells apples for $3 per pound and has a fixed cost of $20 for packaging. Write the equation for the total revenue (R) based on the pounds of apples sold (p). How can you determine the total revenue if 10 pounds are sold?

• $20

• $15

• $40

• $30

A phone company offers a plan that costs $40 per month plus $0.10 for each minute used. If you graph the total cost (C) against the number of minutes (m), what does the slope represent?

• The slope represents the total monthly cost of the plan.

• The slope represents the fixed cost of the plan, which is $40.

• The slope represents the number of minutes used in the month.

• The slope represents the cost per minute, which is $0.10.

A bookstore sells notebooks for $5 each and has a fixed cost of $100 for supplies. Write the equation for the total cost (C) as a function of the number of notebooks (n) sold. How would you find the total cost if 20 notebooks are sold?

• 200

• 150

• 300

• 250

A taxi company charges a flat rate of $3 plus $2 for each mile driven. If you graph the total fare (F) as a function of the distance (d), what does the y-intercept represent in this scenario?

• The initial charge of $3 for getting into the taxi.

• The cost per mile driven.

• The total distance traveled in miles.

• The maximum fare for a taxi ride.

A concert venue has a seating capacity of 500 and sells tickets for $20 each. If the venue sells out, what is the total revenue? Write the equation for total revenue (R) based on the number of tickets sold (t) and interpret the slope.

• $12000

• $8000

• $5000

• Total revenue is $10000.

A local bakery sells cupcakes for $2 each and has a fixed cost of $50 for ingredients. Write the equation for the total cost (C) as a function of the number of cupcakes (c) sold. How can you use this equation to find the cost of selling 30 cupcakes?

• The cost of selling 30 cupcakes is $130.

• The cost of selling 30 cupcakes is $150.

• The cost of selling 30 cupcakes is $90.

• The cost of selling 30 cupcakes is $110.