Graph Linear Equations & Find Intersection Points

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 intersection point that represents the dimensions of the pen.

• Width: 20 meters, Length: 30 meters

• Width: 25 meters, Length: 25 meters

• Width: 30 meters, Length: 20 meters

• Width: 10 meters, Length: 40 meters

A school is planning a field trip and has a budget of $300. The cost per student is represented by the equation y = 15x, where x is the number of students. The total cost for the bus is represented by the equation y = 200. Graph both equations and identify the intersection point that shows how many students can attend the trip.

• 10

• 13

• 20

• 15

A local bakery sells cupcakes for $2 each and cookies for $1 each. If the bakery wants to make $50 in sales, the equation for cupcakes is y = 50 - 2x, and for cookies, it is y = 50 - x. Graph the equations and find the intersection point that shows the combination of cupcakes and cookies sold.

• (0, 50)

• (5, 45)

• (10, 30)

• (25, 0)

A concert venue has a seating capacity of 500. If tickets for adults are $20 and for children are $10, the equation for adult tickets is y = 20x, and for children is y = 10(500 - x). Graph the equations and identify the intersection point that represents the number of adult and child tickets sold.

• Adult tickets: 166, Child tickets: 334

• Adult tickets: 200, Child tickets: 300

• Adult tickets: 150, Child tickets: 350

• Adult tickets: 100, Child tickets: 400

A car rental company charges a flat fee of $30 plus $0.20 per mile driven. The total cost can be represented by the equation y = 30 + 0.2x. Another company charges $25 plus $0.25 per mile. Represent this with the equation y = 25 + 0.25x. Graph both equations and find the intersection point that shows when both companies charge the same amount.

• The intersection point is (120, 55).

• The intersection point is (90, 48).

• The intersection point is (80, 45).

• The intersection point is (100, 50).

A gym offers two membership plans. Plan A costs $40 per month, and Plan B costs $20 per month plus a one-time fee of $100. The equations are y = 40x and y = 20x + 100. Graph the equations and identify the intersection point that shows when both plans cost the same.

• (6, 240)

• (4, 160)

• The intersection point is (5, 200).

• (3, 120)

A bookstore sells novels for $15 each and textbooks for $30 each. If a student has $120 to spend, the equation for novels is y = 120 - 15x, and for textbooks is y = 120 - 30x. Graph both equations and find the intersection point that shows the combination of novels and textbooks the student can buy.

• The student can buy 0 novels and 4 textbooks.

• 2 novels and 2 textbooks

• 3 novels and 1 textbook

• 1 novel and 3 textbooks

A pizza shop sells small pizzas for $10 and large pizzas for $15. If a customer spends $60, the equation for small pizzas is y = 60 - 10x, and for large pizzas is y = 60 - 15x. Graph the equations and identify the intersection point that represents the number of small and large pizzas ordered.

• 3 small pizzas and 1 large pizza

• 2 small pizzas and 2 large pizzas

• 1 small pizza and 3 large pizzas

• 0 small pizzas and 4 large pizzas

A charity event sells tickets for $25 each and has a goal of raising $500. The equation for ticket sales is y = 25x. If they also have a donation box that collects $100, the equation becomes y = 100 + 25x. Graph both equations and find the intersection point that shows how many tickets need to be sold to reach the goal.

• 15

• 25

• 20

• 30

A company produces two types of gadgets. The cost to produce type A is represented by the equation y = 5x, and the cost to produce type B is represented by y = 3x + 10. If the company has a budget of $50, graph both equations and identify the intersection point that shows the maximum number of gadgets that can be produced within the budget.

• The maximum number of gadgets that can be produced is 7 of type B.

• The maximum number of gadgets that can be produced is 3 of type A and 2 of type B.

• The maximum number of gadgets that can be produced is 5 of type A.

• The maximum number of gadgets that can be produced is 10 of type A.