Linear Relationships: Solving for Costs and Interpreting Slope

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation that represents the total cost (C) as a function of miles driven (m). What is the slope and what does it represent?

• C = 50 + 0.20m; Slope = 0.20 (cost per mile)

• C = 50m; Slope = 50 (total cost per mile)

• C = 50 + 0.50m; Slope = 0.50 (cost per mile)

• C = 50 + 0.10m; Slope = 0.10 (cost per mile)

If a cell phone plan costs $30 per month plus $0.10 per text message, write the equation for the total cost (C) based on the number of text messages (t). What is the y-intercept and what does it signify?

• C = 30 + 0.10t; y-intercept = 30, signifies the base cost of the plan.

• C = 0.10t; y-intercept = 30, signifies the total cost without texts.

• C = 30 + 0.05t; y-intercept = 0, signifies no base cost.

• C = 30t + 0.10; y-intercept = 0, signifies no cost without texts.

A gardener charges $15 for a basic service and an additional $5 for each hour of work. Write the equation for the total charge (C) based on hours worked (h). What does the slope represent in this context?

• C = 15 + 5h; the slope represents the additional charge per hour of work.

• C = 15h; the slope represents the total charge.

• C = 5 + 15h; the slope represents the base charge.

• C = 20 + 5h; the slope represents the initial fee.

A gym membership costs $25 per month plus a one-time fee of $100. Write the equation for the total cost (C) based on the number of months (m). What is the y-intercept and what does it indicate?

• C = 25m + 200; y-intercept = 200, indicating a higher initial fee.

• C = 100m + 25; y-intercept = 25, indicating monthly cost.

• C = 25m + 100; y-intercept = 100, indicating the initial fee.

• C = 25m + 50; y-intercept = 50, indicating a discount.

A delivery service charges a base fee of $10 plus $2 for each mile driven. If the total cost is $26, how many miles were driven?

• 10 miles

• 12 miles

• 8 miles

• 5 miles

A phone company offers a plan that costs $40 per month plus $0.05 per minute of calls. If a customer’s bill is $60, how many minutes did they use?

• 400 minutes

• 100 minutes

• 200 minutes

• 50 minutes

A taxi company charges a flat rate of $3 plus $1.50 per mile. If a customer paid $12, how many miles did they travel?

• 4 miles

• 8 miles

• 10 miles

• 6 miles

A subscription service charges $10 per month plus $2 for each additional feature. If a customer pays $26, how many additional features did they choose?

• 8

• 10

• 3

• 5

A school sells tickets for a play at $5 each. If the total revenue from ticket sales is $200, how many tickets were sold? Write the equation and identify the slope.

• 50

• 25

• 40

• 30

A local bakery sells cupcakes for $3 each and has a fixed cost of $50 for supplies. Write the equation for total revenue (R) based on the number of cupcakes sold (c). What does the slope represent in this scenario?

• R = 3c; the slope represents the revenue per cupcake sold.

• R = 50 + 3c; the slope represents the total cost of supplies.

• R = 3c + 50; the slope represents the fixed cost of supplies.

• R = 3c - 50; the slope represents the profit per cupcake sold.