A Resort in California Offers Snorkeling, Paddle Boarding, and Surfing As Shown Below

8.EE.8a (Graphing Systems of Equations)

DEVELOP : (It is assumed that students have the knowledge and skills for writing and graphing linear equations. The purpose of the first TASK is to have students practice plugging values into equations they write and to understand what the ordered pairs represent).

TASK: A resort in California offers snorkeling, paddle boarding, and surfing as shown below.

ACTIVITY FEE COST PER HOUR SNORKELING $5 $5 PADDLE BOARDING $15 $10 SURFING $30 $15

Write an equation to represent the total cost (y) for (x) number of hours spent participating in each activity.

1. SNORKELING: ______2. PADDLE BOARDING: ______3. SURFING: ______4. Find the cost to participate in each activity for 1, 3 and 5 hours. Show each answer as an ordered pair.

HOURS Cost of Cost of PADDLE Cost of Solutions SNORKELING ($) BOARDING ($) SURFING ($) (Ordered Pairs) 1 3 5

5. What do the ordered pairs represent? ______

SOLIDIFY: (The purpose of this TASK is to determine the point of intersection when graphing a system of equations).

TASK: Solve the system of equations y = 2x + 3 and y = 3x – 1 by graphing.

1. Name the point of intersection as an ORDERED PAIR ______2. Substitute the ordered pair into both equations. What do you notice? ______3. Graph each system of equations and determine the point of intersection. Justify your answer.

A) y = x + 1 and y = 2x + 3

Point of intersection: ______

B) 2x + 2y = 8 and y = x - 2

Point of intersection: ______

PRACTICE: (The purpose of this TASK is to have students write a system of equations using a real life example and interpreting what the solution represents).

1. Write a system of equations that represents the following situation and justify your answer:

Johnny is twice as old as Gina. Johnny is five years older than Gina. ______

2. Graph the system of equations:

3. Write the intersection of the system as an ordered pair: ______4. Interpret the solution and find Johnny’s age: ______