Exploring Real-Life Linear Functions: Write & Analyze Equations

A car rental company charges a flat fee of $50 plus $20 for each day you rent a car. Write the equation that represents the total cost (C) as a function of the number of days (d) you rent the car. What is the slope of the line?

• C = 50 + 30d; slope = 30

• C = 50 + 20d; slope = 20

• C = 20d; slope = 20

• C = 50 + 10d; slope = 10

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 equation of the line? What does the slope represent in this context?

• C = 30 + 10c; slope = 10 (cost per class)

• C = 30 + 15c; slope = 15 (cost per class)

• C = 30 + 5c; slope = 5 (cost per class)

• C = 20 + 10c; slope = 10 (cost per class)

A farmer sells apples for $2 per pound. If the total revenue (R) from selling apples is graphed against the number of pounds (p) sold, what is the equation of the line? How would you interpret the slope?

• R = p, slope = 1

• R = 2p + 1, slope = 2

• R = 2p, slope = 2

• R = 3p, slope = 3

A school is planning a field trip and charges a base fee of $100 plus $15 per student. Write the equation for the total cost (C) based on the number of students (s). What does the y-intercept represent in this scenario?

• C = 15 + 100s; The y-intercept represents the cost per student when there are no students.

• C = 100s + 15; The y-intercept represents the total cost for all students.

• C = 100 + 15s; The y-intercept represents the base fee of $100 when there are no students.

• C = 15s; The y-intercept represents the cost when there are no students.

A delivery service charges a flat rate of $5 plus $1.50 for each package delivered. If you were to graph the total charge (C) as a function of the number of packages (p), what would the equation be? What does the slope indicate?

• C = 1.5p; The slope indicates the total charge for all packages.

• C = 5p; The slope indicates the fixed cost of delivery.

• C = 5 + 2p; The slope indicates a discount for multiple packages.

• C = 5 + 1.5p; The slope indicates the additional charge for each package delivered.

A concert venue sells tickets for $25 each and has a fixed cost of $200 for the event. Write the equation for the total revenue (R) based on the number of tickets (t) sold. How would you describe the relationship between tickets sold and revenue?

• R = 25t - 200

• R = 200t

• R = 200 + 25t

• R = 25t

A phone company offers a plan that costs $40 per month plus $0.10 per minute of calls. If you graph the total bill (B) as a function of the number of minutes (m) used, what is the equation? What does the slope represent?

• B = 0.10m; slope = 0.40

• B = 0.10 + 40m; slope = 40

• B = 40 + 0.10m; slope = 0.10

• B = 40m + 0.10; slope = 40

A bookstore has a membership program that charges $15 annually and offers a 20% discount on all purchases. If you graph the total savings (S) as a function of the amount spent (x), what would the equation look like? How does the slope relate to the discount?

• S = 0.15x - 15

• S = 0.2x + 15

• S = 0.2x - 15

• S = 0.25x - 15

A taxi service charges a base fare of $3 plus $2 for each mile driven. Write the equation for the total fare (F) based on the number of miles (m) driven. What does the y-intercept signify in this context?

• F = 5 + 2m; The y-intercept signifies an additional service fee.

• F = 3 + 2m; The y-intercept signifies the base fare of $3.

• F = 3m + 2; The y-intercept signifies the total fare for 3 miles.

• F = 2m; The y-intercept signifies the cost per mile.

A local bakery sells cupcakes for $3 each and has a fixed cost of $50 for ingredients. If you graph the total cost (C) as a function of the number of cupcakes (c) sold, what is the equation? How would you interpret the slope in terms of cost per cupcake?

• C = 3c + 50

• C = 50 + 3c^2

• C = 50c + 3

• C = 3c - 50