Understanding Slope and Graphing Linear Costs

A car rental company charges a flat fee of $20 plus $0.15 per mile driven. Write a linear equation to represent the total cost (C) in terms of miles driven (m). What is the slope of this equation, and what does it represent in this context?

• C = 25 + 0.15m; slope = 0.15, representing the flat fee.

• C = 20 + 0.15m; slope = 0.15, representing the cost per mile.

• C = 20 + 0.10m; slope = 0.10, representing the total cost.

• C = 15 + 0.20m; slope = 0.20, representing the base fee.

If you graph the equation from the previous problem, what would be the y-intercept? Explain its significance in the context of the problem.

• The y-intercept is the slope of the line.

• The y-intercept is the point where the line crosses the x-axis.

• The y-intercept is the value of y when x = 0.

• The y-intercept is the value of x when y = 0.

A gardener plants 5 trees in the first week and 3 more trees each subsequent week. Write a linear equation to represent the number of trees (T) planted after w weeks. What does the slope represent in this scenario?

• T = 5w + 2; slope = 5

• T = 3w + 2; slope = 3 (trees per week after the first week)

• T = 2w + 3; slope = 2

• T = 3w + 5; slope = 2

Using the equation from the previous question, graph the number of trees planted over time. What does the slope of the graph indicate about the gardener's planting rate?

• The slope shows the total number of trees planted.

• The slope indicates the height of the trees planted.

• The slope indicates the gardener's planting rate.

• The slope represents the gardener's total expenses.

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

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

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

• C = 0.10t; the slope represents the number of text messages.

• C = 30 + 0.05t; the slope represents the monthly fee.

Graph the equation from the previous problem. Identify the y-intercept and explain its meaning in the context of the phone plan.

• The y-intercept is the fixed cost of the phone plan.

• The y-intercept shows the monthly payment for additional features.

• The y-intercept indicates the maximum data limit.

• The y-intercept represents the total cost after usage.

A school is planning a field trip and charges $15 per student plus a one-time bus fee of $100. Write a linear equation for the total cost (C) based on the number of students (s). What does the slope represent?

• C = 15s; The slope represents the fixed bus fee.

• C = 15s + 100; The slope represents the cost per additional student.

• C = 20s + 50; The slope represents the cost per student discount.

• C = 10s + 100; The slope represents the total cost.

Using the equation from the previous question, create a graph showing the total cost for different numbers of students. What does the slope tell you about the cost per student?

• The slope represents the total number of students.

• The slope shows the average cost of all students combined.

• The slope indicates the cost per student.

• The slope indicates the fixed cost regardless of the number of students.

A local gym charges a $50 membership fee plus $5 per class attended. Write the linear equation for the total cost (C) based on the number of classes (c) attended. What does the slope indicate?

• C = 50 - 5c

• C = 50 + 5c

• C = 5c

• C = 50 + 10c

Graph the equation from the previous problem. Discuss the significance of the slope and the y-intercept in the context of gym membership costs.

• The slope shows the total number of gym members.

• The y-intercept indicates the monthly fee for gym classes.

• The slope indicates the rate of increase in membership costs, while the y-intercept represents the initial cost of joining the gym.

• The slope represents the average age of gym members.