Exploring Slope and Intercept in Real-Life Scenarios

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. Write the equation for the total cost (C) in terms of miles driven (m). What is the slope and what does it represent?

• C = 30 + 0.20m; Slope = 0.20 (cost per mile)

• C = 30 + 0.20m; Slope = 30 (fixed cost)

• C = 30 + 0.10m; Slope = 0.10 (cost per mile)

• C = 30 + 0.50m; Slope = 0.50 (cost per mile)

A local gym charges a monthly membership fee of $50 and an additional $10 for each fitness class attended. Write the equation for the total cost (C) in terms of classes attended (c). What is the y-intercept and what does it represent?

• C = 50 + 10c; y-intercept = 50, representing the base membership fee.

• C = 50c + 10; y-intercept = 10, representing the cost per class.

• C = 10 + 50c; y-intercept = 10, representing the total cost of classes.

• C = 50 + 5c; y-intercept = 50, representing a discount on classes.

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 their total earnings (E) based on the number of cups sold (x). Are their lines parallel or perpendicular?

• E_A = 2x + 1 and E_B = 3x + 1; lines are perpendicular

• The equations are E_A = 2x and E_B = 3x. The lines are neither parallel nor perpendicular.

• E_A = 3x and E_B = 2x; lines are parallel

• E_A = 2x and E_B = 2x; lines are parallel

A school is planning a field trip. The cost per student is $15 for transportation and $5 for admission. Write the equation for the total cost (C) in terms of the number of students (s). What is the slope and what does it represent?

• C = 15s + 5

• C = 20s

• C = 10s

• C = 25s

A taxi company charges a base fare of $4 plus $1.50 per mile. Write the equation for the total fare (F) in terms of miles driven (m). If another taxi company charges a base fare of $5 plus $1.50 per mile, are their lines parallel or perpendicular?

• The lines are parallel.

• The lines intersect at a right angle.

• The lines are perpendicular.

• The lines are not related.

A farmer sells apples for $1.50 per pound and oranges for $2.00 per pound. Write the equations for the total revenue (R) from selling apples (a) and oranges (o). How do the slopes compare?

• R = 1.50a for apples and R = 2.00o for oranges; the slope for oranges (2.00) is greater than for apples (1.50).

• R = 1.50o for oranges and R = 2.00a for apples; the slope for apples (2.00) is greater than for oranges (1.50).

• R = 1.50a + 2.00o; the slope for apples (1.50) is less than for oranges (2.50).

• R = 1.00a for apples and R = 2.50o for oranges; the slopes are equal.

A concert venue has a seating capacity of 500. If tickets are sold for $20 each, write the equation for total revenue (R) in terms of tickets sold (t). What is the y-intercept and what does it represent?

• R = 25t; y-intercept = 500, representing total revenue at full capacity.

• R = 10t; y-intercept = 10, representing revenue when 10 tickets are sold.

• R = 20t; y-intercept = 0, representing no revenue when no tickets are sold.

• R = 20t + 100; y-intercept = 100, representing a base revenue regardless of ticket sales.

A delivery service charges a flat fee of $10 plus $0.50 per mile. Write the equation for the total cost (C) in terms of miles driven (m). What does the slope represent in this context?

• C = 10 + 0.25m; the slope represents the total cost.

• C = 10 + 1.00m; the slope represents the delivery fee.

• C = 5 + 0.50m; the slope represents the distance traveled.

• C = 10 + 0.50m; the slope represents the cost per mile.

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.

• perpendicular

• intersecting

• parallel

• coincident

A local bakery sells cupcakes for $3 each and cookies for $2 each. Write the equations for the total revenue (R) from selling cupcakes (c) and cookies (k). How do the slopes of these lines compare?

• The slope for cookies (3) is greater than the slope for cupcakes (2).

• The slope for cupcakes (2) is less than the slope for cookies (3).

• The slopes for both cupcakes and cookies are equal (3).

• The slope for cupcakes (3) is greater than the slope for cookies (2).