Understanding Slope & Intercepts in Real-Life Scenarios

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

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

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

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

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

Two friends are selling lemonade. Friend A sells lemonade for $2 per cup, while Friend B sells it for $3 per cup. Write the equations for the total revenue (R) for each friend based on the number of cups sold (c). Are the lines parallel or perpendicular?

• The lines are intersecting.

• The lines are vertical.

• The lines are coincident.

• The lines are parallel.

A gym charges a monthly fee of $30 plus $10 for each class attended. Write the equation for the total cost (C) in terms of classes attended (x). What is the y-intercept and what does it signify?

• C = 30 + 10x; y-intercept = 30, signifies the monthly fee.

• C = 50 + 5x; y-intercept = 50, signifies an annual fee.

• C = 10x; y-intercept = 10, signifies the cost per class.

• C = 30x; y-intercept = 0, signifies no monthly fee.

A local bakery sells muffins for $1.50 each and cookies for $2.00 each. If the total revenue from selling muffins and cookies is represented by the equation R = 1.5m + 2c, where m is muffins and c is cookies, what is the slope of the line?

• 3.0

• 2.0

• 1.5

• 1.0

A school is planning a fundraiser. They can sell tickets for $5 each or $8 each. Write the equations for the total revenue from each ticket type. How do the slopes compare?

• The slope for $5 tickets is greater than $8 tickets.

• The slopes are 5 for $5 tickets and 10 for $8 tickets; the slope for $5 tickets is greater.

• The slopes are both 5; there is no difference.

• The slopes are 5 for $5 tickets and 8 for $8 tickets; the slope for $8 tickets is greater.

A taxi company charges a base fare of $3 plus $2 per mile. Write the equation for the total fare (F) in terms of miles driven (d). What does the slope represent in this scenario?

• F = 2d; the slope represents the total fare.

• F = 3 + 2d; the slope represents the cost per mile driven.

• F = 3 + d; the slope represents the base fare.

• F = 3 + 3d; the slope represents the distance driven.

Two lines are represented by the equations y = 2x + 3 and y = -0.5x + 1. Are these lines parallel, perpendicular, or neither? Explain your reasoning.

• intersecting

• parallel

• coincident

• perpendicular

A farmer sells apples for $1.20 per pound and oranges for $0.80 per pound. If the total revenue is represented by the equation R = 1.2a + 0.8o, where a is pounds of apples and o is pounds of oranges, what is the slope of the line?

• 0.8

• 1.2

• 1.0

• 1.5

A concert venue has a seating capacity of 500. If tickets are sold for $20 each, write the equation for total revenue (R) based on the number of tickets sold (t). What does the y-intercept represent?

• R = 20t; The y-intercept represents $0 in revenue when no tickets are sold.

• R = 10t; The y-intercept represents $10 in revenue when no tickets are sold.

• R = 25t; The y-intercept represents $500 in revenue when no tickets are sold.

• R = 20t + 100; The y-intercept represents $100 in revenue when no tickets are sold.

A delivery service charges a flat fee of $15 plus $0.50 per mile. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and what does it indicate about the cost structure?

• C = 15 + 0.50m; Slope = 0.50, indicating cost increases by $0.50 per mile.

• C = 10 + 0.75m; Slope = 0.75, indicating cost increases by $0.75 per mile.

• C = 20 + 0.25m; Slope = 0.25, indicating cost increases by $0.25 per mile.

• C = 15 + 1.00m; Slope = 1.00, indicating cost increases by $1.00 per mile.