Exploring Real-Life Linear Equations and Graphs

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). Graph this equation and analyze how the cost changes with distance.

• C = 0.20m - 50

• C = 50 + 0.20m

• C = 50 - 0.20m

• C = 50 + 0.50m

Maria is saving money to buy a new bike. She saves $15 each week. Write a linear equation to represent the total amount saved (S) after w weeks. How many weeks will it take for her to save $120? Graph the equation and analyze the slope.

• 10 weeks

• 8 weeks

• 12 weeks

• 6 weeks

A store sells notebooks for $2 each and pens for $1 each. If a student buys a total of 10 items and spends $16, write a system of linear equations to represent this situation. Graph the equations and find the number of notebooks and pens purchased.

• Notebooks: 4, Pens: 6

• Notebooks: 7, Pens: 3

• Notebooks: 6, Pens: 4

• Notebooks: 5, Pens: 5

A gardener is planting flowers in a rectangular garden. The length of the garden is twice its width. If the perimeter of the garden is 48 meters, write a linear equation to find the dimensions of the garden. Graph the equation and analyze the relationship between length and width.

• Width: 10 meters, Length: 20 meters

• Width: 6 meters, Length: 12 meters

• Width: 8 meters, Length: 16 meters

• Width: 12 meters, Length: 24 meters

A local bakery sells cupcakes for $3 each and cookies for $2 each. If a customer buys a total of 15 items and spends $36, write a system of linear equations to represent this situation. Graph the equations and determine how many cupcakes and cookies were bought.

• 5 cupcakes and 10 cookies

• 7 cupcakes and 8 cookies

• 4 cupcakes and 11 cookies

• 6 cupcakes and 9 cookies

A fitness center charges a monthly fee of $40 plus $5 for each class attended. Write a linear equation to represent the total cost (C) based on the number of classes (c) attended. How much will it cost if a member attends 10 classes? Graph the equation and analyze the cost per class.

• $70

• $50

• $100

• $90

A taxi company charges a base fare of $3 plus $2 per mile. Write a linear equation to represent the total fare (F) based on the number of miles (m) traveled. If a passenger travels 5 miles, what will the fare be? Graph the equation and analyze the fare structure.

• $13

• $8

• $15

• $10

A bookstore sells novels for $10 each and magazines for $5 each. If a customer buys a total of 8 items and spends $50, write a system of linear equations to represent this situation. Graph the equations and find the number of novels and magazines purchased.

• 2 novels and 6 magazines

• 1 novel and 7 magazines

• 4 novels and 4 magazines

• 3 novels and 5 magazines