Linear Equations and Graphing: Real-World Applications

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a linear equation to represent the total cost (C) in terms of miles driven (m).

• C = 50 + 0.20m

• C = 50 - 0.20m

• C = 50 + 0.50m

• C = 0.20 + 50m

If you graph the equation from the previous problem, what would be the y-intercept and what does it represent in this context?

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

• The y-intercept represents the maximum value of y.

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

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

A gym charges a monthly membership fee of $30 plus $10 for each class attended. Write the linear equation for the total cost (C) based on the number of classes (c) attended.

• C = 30 + 10c

• C = 10c - 30

• C = 10 + 30c

• C = 30c + 10

Using the equation from the previous problem, how much would it cost to attend 5 classes?

• 3X

• 5X

• 10X

• X5

A store sells notebooks for $2 each and pens for $1 each. If you buy a total of 10 items for $16, write a system of linear equations to represent this situation.

• x + y = 8, 2x + 2y = 16

• x + y = 10, 3x + y = 16

• x + y = 10, 2x + y = 16

• x + y = 12, 2x + y = 14

Graph the system of equations from the previous problem. What do the intersection points represent?

• The intersection points show the maximum values of the equations.

• The intersection points represent the x-intercepts of the equations.

• The intersection points indicate where the lines are parallel.

• The intersection points represent the solutions to the system of equations.

A gardener plants flowers in rows. Each row contains 4 flowers, and the total number of flowers planted is 28. Write a linear equation to represent the relationship between the number of rows (r) and the total number of flowers (f).

• f = 28 - r

• f = 4r + 4

• r + 4 = 28

• 4r = 28

If the gardener wants to plant 40 flowers, how many rows will he need? Use the equation from the previous problem to find the answer.

• 5

• 6

• 8

• 4

A phone plan costs $25 per month plus $0.10 per minute used. Write a linear equation to represent the total cost (C) based on the number of minutes (m) used.

• C = 25m + 0.10

• C = 25 + 0.05m

• C = 25 + 0.10m

• C = 0.10 + 25m

If you graph the equation from the previous problem, what does the slope represent in the context of the phone plan?

• The slope indicates the total cost of the phone plan.

• The slope represents the cost per unit of usage in the phone plan.

• The slope shows the maximum data limit allowed.

• The slope represents the fixed monthly fee of the plan.