Slope & Intercept: Real-World Equation Challenges

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 intercept?

• C = 20 + 0.20m; Slope: 0.20, Intercept: 20

• C = 30 + 0.50m; Slope: 0.50, Intercept: 30

• C = 30 + 0.10m; Slope: 0.10, Intercept: 30

• C = 30 + 0.20m; Slope: 0.20, Intercept: 30

A gym charges a monthly membership fee of $25 and an additional $5 per class attended. Write the equation for the total cost (C) in terms of classes attended (c). Identify the slope and intercept.

• C = 30 + 5c; Slope: 5, Intercept: 30

• C = 25 + 10c; Slope: 10, Intercept: 25

• C = 20 + 5c; Slope: 5, Intercept: 20

• C = 25 + 5c; Slope: 5, Intercept: 25

Two friends are saving money for a concert. Friend A saves $10 a week, while Friend B saves $15 a week. Write the equations for the total savings of each friend after w weeks. What are the slopes and intercepts?

• Friend A: slope = 10, intercept = 0; Friend B: slope = 15, intercept = 0

• Friend A: slope = 10, intercept = 10; Friend B: slope = 15, intercept = 5

• Friend A: slope = 10, intercept = 5; Friend B: slope = 15, intercept = 10

• Friend A: slope = 5, intercept = 0; Friend B: slope = 20, intercept = 0

A phone plan costs $40 per month plus $0.10 per text message. Write the equation for the total cost (C) in terms of text messages (t). Identify the slope and intercept.

• C = 40 + 0.10t; Slope: 0.10, Intercept: 40

• C = 40 + 0.20t; Slope: 0.20, Intercept: 40

• C = 40 + 0.05t; Slope: 0.05, Intercept: 40

• C = 30 + 0.10t; Slope: 0.10, Intercept: 30

A bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 10 items for $24, write a system of equations to represent the situation. What are the slopes and intercepts of each equation?

• x + y = 12, 3x + 2y = 30; Slopes: -1 (first), -1 (second); Intercepts: 12 (first), 15 (second)

• System of equations: x + y = 10, 3x + 2y = 24; Slopes: -1 (first), -1.5 (second); Intercepts: 10 (first), 12 (second)

• x + y = 8, 3x + 2y = 20; Slopes: -1 (first), -1.2 (second); Intercepts: 8 (first), 10 (second)

• x + y = 10, 2x + 3y = 24; Slopes: -1.5 (first), -0.67 (second); Intercepts: 10 (first), 8 (second)

A school is selling tickets for a play. Adult tickets are $12 and student tickets are $8. If they sell a total of 50 tickets for $480, write a system of equations to represent the situation. Identify the slopes and intercepts.

• x + y = 60; 10x + 8y = 480; Slopes: -1 (first), -1.25 (second); Intercepts: 60 (first), 60 (second)

• x + y = 50; 12x + 8y = 500; Slopes: -1 (first), -1.5 (second); Intercepts: 50 (first), 62.5 (second)

• x + y = 40; 12x + 10y = 480; Slopes: -1 (first), -1.2 (second); Intercepts: 40 (first), 48 (second)

• x + y = 50; 12x + 8y = 480; Slopes: -1 (first), -1.5 (second); Intercepts: 50 (first), 60 (second)

A taxi company charges a base fare of $2.50 plus $1.50 per mile. Write the equation for the total fare (F) in terms of miles (m). What is the slope and intercept?

• F = 1.50m; slope = 2.50, intercept = 0

• F = 2.50m + 1.50; slope = 2.50, intercept = 1.50

• F = 1.50 + 2.50m; slope = 1.50, intercept = 1.50

• F = 2.50 + 1.50m; slope = 1.50, intercept = 2.50

A landscaping company charges a flat fee of $100 plus $25 per hour of work. Write the equation for the total cost (C) in terms of hours worked (h). Identify the slope and intercept.

• C = 100 + 15h; Slope = 15, Intercept = 100

• C = 50 + 30h; Slope = 30, Intercept = 50

• C = 100 + 20h; Slope = 20, Intercept = 100

• C = 100 + 25h; Slope = 25, Intercept = 100

A local theater sells adult tickets for $15 and child tickets for $10. If they sold a total of 100 tickets for $1200, write a system of equations to represent the situation. What are the slopes and intercepts?

• x + y = 150 and 15x + 5y = 1200

• The system of equations is: x + y = 100 and 15x + 10y = 1200. Slopes: -1 (first equation), -1.5 (second equation). Intercepts: 100 (first equation), 120 (second equation).

• x + y = 80 and 20x + 10y = 1000

• x + y = 100 and 10x + 15y = 1200

A subscription box service charges $20 per month plus $5 for each additional item. Write the equation for the total cost (C) in terms of additional items (i). Identify the slope and intercept.

• C = 15 + 5i; slope = 5, intercept = 15

• C = 20 + 5i; slope = 5, intercept = 20

• C = 25 + 5i; slope = 5, intercept = 25

• C = 20 + 10i; slope = 10, intercept = 20