Solving Linear Costs: Y-Intercepts and Slope Changes

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the equation for the total cost (y) in terms of miles driven (x). What is the y-intercept?

• The y-intercept is 100.

• The y-intercept is 0.

• The y-intercept is 20.

• The y-intercept is 50.

A gym membership costs $30 to join and $15 per month. Write the equation for the total cost (y) after x months. What does the y-intercept represent in this context?

• y = 30x + 15; The y-intercept represents the total cost after one month.

• y = 15 + 30x; The y-intercept represents the cost after x months.

• y = 15x; The y-intercept represents the monthly fee of $15.

• y = 30 + 15x; The y-intercept represents the initial joining fee of $30.

A delivery service charges a base fee of $10 plus $2 for each package delivered. Write the equation for the total cost (y) in terms of packages delivered (x). How does changing the base fee affect the slope?

• y = 10 + 2x; Changing the base fee affects the y-intercept, not the slope.

• y = 10 + x; Changing the base fee increases the slope.

• y = 2 + 10x; Changing the base fee affects both the slope and y-intercept.

• y = 2x; Changing the base fee has no effect on the slope.

A school is selling tickets for a play at $5 each. If they have a fixed cost of $200 for the venue, write the equation for total revenue (y) in terms of tickets sold (x). What is the slope of this equation?

• y = 5x; slope = 5

• y = 5x + 200; slope = 5

• y = 10x; slope = 10

• y = 200 + 5x; slope = 200

A phone plan costs $25 per month plus $0.10 per text message. Write the equation for the total cost (y) in terms of text messages sent (x). What does the slope represent?

• y = 25x + 0.10; slope represents the total monthly cost.

• y = 25 + 0.10x; slope represents the cost per text message.

• y = 0.10 + 25x; slope represents the base cost of the plan.

• y = 0.10x; slope represents the total cost without base fee.

A local bakery sells cupcakes for $3 each and has a daily fixed cost of $50. Write the equation for total sales (y) in terms of cupcakes sold (x). What is the y-intercept and what does it signify?

• y = 3x - 30; y-intercept = -30, signifies variable costs.

• y = 3x; y-intercept = 0, signifies no fixed costs.

• y = 3x - 50; y-intercept = -50, signifies fixed costs.

• y = 3x + 50; y-intercept = 50, signifies profit.

A taxi company charges a $2 flag drop fee and $1.50 per mile. Write the equation for the total fare (y) in terms of miles driven (x). How does the slope change if the per-mile charge increases?

• y = 1.50 + 2x; slope remains constant regardless of charge.

• y = 2 + 0.50x; slope decreases with lower per-mile charge.

• y = 2 + 2x; slope decreases with higher per-mile charge.

• y = 2 + 1.50x; slope increases with higher per-mile charge.

A subscription service charges $10 per month plus a one-time setup fee of $20. Write the equation for total cost (y) in terms of months (x). What does the y-intercept indicate?

• y = 10x - 20; The y-intercept indicates the monthly fee of $10.

• y = 10x + 20; The y-intercept indicates the one-time setup fee of $20.

• y = 20x + 10; The y-intercept indicates the total cost after one month.

• y = 10x + 10; The y-intercept indicates the total cost for two months.

A farmer sells apples for $2 per pound and has fixed costs of $100 for equipment. Write the equation for total revenue (y) in terms of pounds sold (x). How does the slope reflect the price per pound?

• y = 100 + 2x

• y = 2x + 100

• y = 2x

• y = 2x - 100

A concert venue charges $100 for renting the space plus $5 per ticket sold. Write the equation for total income (y) in terms of tickets sold (x). What does the slope tell you about the income per ticket?

• y = 100 + 10x; The slope of 10 indicates an income increase of $10 per ticket sold.

• y = 50 + 5x; The slope of 5 indicates an income increase of $5 per ticket sold.

• y = 100 - 5x; The slope of -5 indicates a loss of $5 per ticket sold.

• y = 100 + 5x; The slope of 5 indicates an income increase of $5 per ticket sold.