Graphing Linear Equations: Real-Life Applications in 8th Grade

A farmer has 100 meters of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by the equation y = 50 - x, where x is the width, graph the equations and find the dimensions of the pen.

• 40 meters (width) and 10 meters (length)

• 20 meters (width) and 30 meters (length)

• 25 meters (width) and 25 meters (length)

• 30 meters (width) and 20 meters (length)

Two friends, Alex and Jamie, are selling lemonade and cookies. Alex sells lemonade for $2 per cup and Jamie sells cookies for $1 each. If they want to make a total of $20, graph the equations and identify how many cups of lemonade and cookies they need to sell.

• 15 cups of lemonade and 2 cookies

• 0 cups of lemonade and 20 cookies

• 5 cups of lemonade and 5 cookies

• They can sell 10 cups of lemonade and 0 cookies, or any combination of lemonade and cookies that satisfies 2x + y = 20.

A school is planning a field trip and has a budget of $300. The cost per student for the bus is $10 and for admission is $15. Write the equations, graph them, and find the maximum number of students that can attend the trip.

• 20

• 15

• 12

• 10

A local gym charges a monthly fee of $30 plus $5 per class attended. Another gym charges a flat fee of $50. Graph the equations and determine how many classes need to be attended for the first gym to be cheaper than the second.

• 4 classes

• 3 classes

• 5 classes

• 2 classes

A concert venue has two pricing options: Option A charges $25 per ticket and Option B charges a flat fee of $100 for up to 5 tickets. Graph the equations and find the number of tickets where both options cost the same.

• 6

• 5

• 4

• 3

A bookstore sells novels for $10 each and textbooks for $20 each. If a student has $100 to spend, graph the equations and determine how many novels and textbooks they can buy without exceeding their budget.

• The student can buy 15 novels and no textbooks.

• The student can buy 8 textbooks and 2 novels.

• The student can buy 12 novels and 3 textbooks.

• The student can buy up to 10 novels, 5 textbooks, or any combination of novels and textbooks that does not exceed the budget.

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Another company charges a flat fee of $30 plus $0.25 per mile. Graph the equations and find the point where both companies charge the same amount.

• Both companies charge the same amount at 500 miles for a total cost of $150.

• Both companies charge the same amount at 200 miles for a total cost of $80.

• Both companies charge the same amount at 300 miles for a total cost of $90.

• Both companies charge the same amount at 400 miles for a total cost of $130.

A pizza shop sells small pizzas for $8 and large pizzas for $12. If a family wants to spend no more than $40, graph the equations and find the combinations of small and large pizzas they can order.

• The combinations of small and large pizzas they can order are: (0 small, 3 large), (1 small, 2 large), (2 small, 1 large), (3 small, 0 large).

• (4 small, 0 large)

• (2 small, 2 large)

• (0 small, 4 large)

A charity event is selling tickets for $15 each and snacks for $5 each. If they want to raise at least $200, graph the equations and find the minimum number of tickets and snacks they need to sell.

• At least 10 tickets and 10 snacks.

• At least 20 tickets and 0 snacks.

• At least 15 tickets and 5 snacks.

• At least 5 tickets and 30 snacks.

A local bakery sells muffins for $3 each and cupcakes for $4 each. If they want to make at least $60 in sales, graph the equations and determine the combinations of muffins and cupcakes they can sell.

• They can only sell 10 muffins and 5 cupcakes.

• The combinations of muffins and cupcakes that can be sold are all points (x, y) in the region defined by 3x + 4y >= 60, including points like (0, 15), (20, 0), and any integer combinations that satisfy the inequality.

• The only combination is (0, 15) for cupcakes.

• Selling 15 muffins and 0 cupcakes is not allowed.