Finding Intersection Points in Real-Life Graphs

A local park is shaped like a rectangle. The length is represented by the equation y = 2x + 3, and the width is represented by y = -x + 10. Graph both equations and identify the intersection point. What does this point represent in the context of the park?

• The intersection point is (4, 12).

• The intersection point is (5, 15).

• The intersection point is (7/3, 23/3).

• The intersection point is (3, 9).

A school is planning to sell tickets for a concert. The cost of tickets can be represented by the equation y = 5x, where x is the number of tickets sold. Another fundraiser sells snacks represented by y = 3x + 10. Graph both equations and find the intersection point. What does this point indicate about ticket and snack sales?

• The intersection point is (2, 10).

• The intersection point is (5, 25).

• The intersection point is (3, 15).

• The intersection point is (10, 50).

A car rental company charges a flat fee of $20 plus $0.50 per mile driven, represented by the equation y = 0.5x + 20. Another company charges $15 plus $0.75 per mile, represented by y = 0.75x + 15. Graph both equations and identify the intersection point. What does this point mean for customers?

• The intersection point is (30, 40), meaning both companies charge $40 for 30 miles.

• The intersection point is (10, 25), meaning both companies charge $25 for 10 miles.

• The intersection point is (20, 30), meaning both companies charge $30 for 20 miles.

• The intersection point is (15, 25), meaning both companies charge $25 for 15 miles.

Two friends are saving money for a concert. Friend A saves $10 a week, represented by y = 10x. Friend B saves $15 a week, represented by y = 15x - 5. Graph both equations and find the intersection point. What does this point tell you about their savings?

• The intersection point is (3, 30), meaning both friends will have saved $30 after 3 weeks.

• The intersection point is (0, 5), meaning Friend B will have saved $5 before starting to save.

• The intersection point is (2, 20), meaning both friends will have saved $20 after 2 weeks.

• The intersection point is (1, 10), meaning both friends will have saved $10 after 1 week.

A farmer is planting two types of crops. The first crop yields 3 bushels per acre, represented by y = 3x. The second crop yields 2 bushels per acre plus a fixed yield of 5 bushels, represented by y = 2x + 5. Graph both equations and identify the intersection point. What does this point represent?

• The intersection point is (5, 15).

• The intersection point is (6, 18).

• The intersection point is (4, 12).

• The intersection point is (3, 9).

A delivery service charges a base fee of $10 plus $2 per mile, represented by y = 2x + 10. Another service charges a base fee of $5 plus $3 per mile, represented by y = 3x + 5. Graph both equations and find the intersection point. What does this point indicate about the cost of delivery?

• The intersection point is (5, 20), indicating both services charge $20 for a 5-mile delivery.

• The intersection point is (6, 22), indicating both services charge $22 for a 6-mile delivery.

• The intersection point is (4, 18), indicating both services charge $18 for a 4-mile delivery.

• The intersection point is (3, 19), indicating both services charge $19 for a 3-mile delivery.

A bookstore sells novels for $12 each, represented by y = 12x. A second bookstore sells the same novels for $10 each plus a $5 membership fee, represented by y = 10x + 5. Graph both equations and identify the intersection point. What does this point mean for customers?

• The intersection point is (3, 36), meaning customers pay the same price for 3 novels at both bookstores.

• The intersection point is (4, 48), meaning customers pay the same price for 4 novels at both bookstores.

• The intersection point is (2, 24), meaning customers pay the same price for 2 novels at both bookstores.

• The intersection point is (1, 12), meaning customers pay the same price for 1 novel at both bookstores.

A gym charges a monthly fee of $30 plus $5 per class, represented by y = 5x + 30. Another gym charges a flat fee of $50 with no class fees, represented by y = 50. Graph both equations and find the intersection point. What does this point indicate about gym membership costs?

• The intersection point is (4, 50), indicating both gyms cost the same after 4 classes.

• The intersection point is (3, 45), indicating both gyms cost the same after 3 classes.

• The intersection point is (5, 55), indicating the second gym is always more expensive.

• The intersection point is (2, 40), indicating the first gym is cheaper after 2 classes.

A local bakery sells cupcakes for $3 each, represented by y = 3x. Another bakery sells them for $2 each plus a $10 setup fee, represented by y = 2x + 10. Graph both equations and identify the intersection point. What does this point represent for customers?

• The intersection point is (20, 60), suggesting both bakeries have the same price for 20 cupcakes.

• The intersection point is (5, 15), meaning the first bakery is cheaper for 5 cupcakes.

• The intersection point is (15, 45), indicating the second bakery offers a better deal for 15 cupcakes.

• The intersection point is (10, 30), meaning both bakeries charge the same price for 10 cupcakes.

A tech company sells laptops for $800 each, represented by y = 800x. Another company sells them for $750 each plus a $100 setup fee, represented by y = 750x + 100. Graph both equations and find the intersection point. What does this point indicate about the pricing of laptops?

• The intersection point is (3, 2400), indicating both companies charge $2400 for 3 laptops.

• The intersection point is (1, 800), indicating both companies charge $800 for 1 laptop.

• The intersection point is (2, 1600), indicating both companies charge $1600 for 2 laptops.

• The intersection point is (0, 100), indicating both companies charge $100 for 0 laptops.