Understanding Slopes and Intercepts in Linear Graphs

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write the linear equation that represents 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 = 1.00

• C = 50 + 0.20m; slope = 0.20

• C = 50 + 0.50m; slope = 0.50

• C = 50 + 0.10m; slope = 0.10

A gardener is planting flowers in a straight line. If he plants 5 flowers every hour, write the linear equation that represents the number of flowers (F) planted after h hours. What is the y-intercept and what does it signify?

• F = 5h + 1; y-intercept = 1, signifies 1 flower planted at the start.

• F = 3h; y-intercept = 2, signifies 2 flowers planted at the start.

• F = 5h; y-intercept = 0, signifies no flowers planted at the start.

• F = 10h; y-intercept = 5, signifies 5 flowers planted at the start.

A phone plan costs $30 per month plus $0.10 per text message sent. Write the equation for the total cost (C) based on the number of text messages (t). What does the slope represent?

• C = 30 + 0.10t; the slope represents the cost per text message.

• C = 30 + 0.05t; the slope represents the discount on text messages.

• C = 0.10 + 30t; the slope represents the fixed cost of the plan.

• C = 30t + 0.10; the slope represents the total monthly cost.

A store sells notebooks for $2 each and charges a $5 service fee. Write the linear equation for the total cost (C) in terms of the number of notebooks (n). What is the y-intercept and what does it mean?

• C = 2n; y-intercept = 2, meaning a cost for each notebook.

• C = 3n + 5; y-intercept = 0, meaning no service fee.

• C = 2n + 5; y-intercept = 5, meaning the service fee when no notebooks are purchased.

• C = 2n + 10; y-intercept = 10, meaning a higher service fee.

A taxi charges a base fare of $3 plus $1.50 for each mile driven. Write the equation for the total fare (F) based on miles driven (m). What does the slope indicate about the cost?

• F = 3m + 1.50; The slope (3) indicates the cost per mile.

• F = 3 + 1.50m; The slope (1.50) indicates the cost per mile.

• F = 3 + 2m; The slope (2) indicates the total fare.

• F = 1.50 + 3m; The slope (3) indicates the base fare.

A school is organizing a field trip. The cost per student is $15, and there is a fixed cost of $200 for the bus. Write the equation for the total cost (C) in terms of the number of students (s). What does the y-intercept represent?

• C = 15s + 200; The y-intercept represents the fixed cost of $200.

• C = 15s + 100; The y-intercept represents the cost of the bus.

• C = 15s; The y-intercept represents the cost per student.

• C = 10s + 200; The y-intercept represents the total cost per student.

A delivery service charges a flat fee of $10 plus $0.50 per package delivered. Write the linear equation for the total charge (C) based on the number of packages (p). What does the slope tell you about the cost?

• C = 10 + 0.25p; The slope (0.25) indicates the cost increases by $0.25 for each additional package.

• C = 10 + 1.00p; The slope (1.00) indicates the cost increases by $1.00 for each additional package.

• C = 5 + 0.50p; The slope (0.50) indicates the cost increases by $0.50 for each additional package.

• C = 10 + 0.50p; The slope (0.50) indicates the cost increases by $0.50 for each additional package.

A fitness center charges a monthly fee of $25 plus $5 for each class attended. Write the equation for the total cost (C) in terms of the number of classes (c). What does the y-intercept represent in this scenario?

• C = 25 + 5c; The y-intercept represents the monthly fee of $25.

• C = 30 + 5c; The y-intercept represents the initial sign-up fee.

• C = 25c; The y-intercept represents the total cost for all classes.

• C = 5c; The y-intercept represents the cost per class.

A concert ticket costs $40, and there is an additional $10 service fee. Write the equation for the total cost (C) in terms of the number of tickets (t). What does the slope indicate?

• C = 40t; The slope indicates that for each additional ticket, the total cost remains the same.

• C = 30t + 10; The slope indicates that for each additional ticket, the total cost increases by $30.

• C = 50t + 10; The slope indicates that for each additional ticket, the total cost increases by $50.

• C = 40t + 10; The slope indicates that for each additional ticket, the total cost increases by $40.

A local bakery sells cupcakes for $3 each and charges a $10 delivery fee. Write the linear equation for the total cost (C) based on the number of cupcakes (c). What does the y-intercept signify in this context?

• C = 3c; y-intercept signifies the price of each cupcake.

• C = 3c + 10; y-intercept signifies the $10 delivery fee.

• C = 5c + 10; y-intercept signifies the cost of ingredients.

• C = 3c + 5; y-intercept signifies a discount on delivery.