Unit 3: Lesson 2 : Graphs of Proportional Relationships

Unit 3: Lesson 2 : Graphs of Proportional Relationships

I Can Learning Goals

• I can graph a proportional relationship from an equation.

• I can tell when two graphs are of the same proportional relationship even if the scales are different.

Open Ended

Warm-Up: Write an equation for this graph.

Possible Responses

•  $y=\ 1\frac{3}{4}x$  

•  $y=\ 1.75x$  

•  $y=\frac{7}{4}x$  

Task 1: Card Sort

• I will give you 12 proportional relationship graphs.

• Write the equation for each graph. Some graphs may have the same equation. You can group the ones that will have the same equation.

Possible Responses

•  $A;\ y=\ 0.25x$  

•  $B,E,H;\ y=3x$  

•  $C,D,G,K;\ y=3.5x$  

•  $I,L;\ y=\frac{4}{3}x$  

•  $F,J;\ y=\frac{5}{2}x$  

Task 2

Two large water tanks are filling with water. Tank A is not filled at a constant rate, and the relationship between its volume of water and time is graphed on each set of axes. Tank B is filled at a constant rate of 1/2  liters per minute. The relationship between its volume of water and time can be described by the equation  $v=\frac{1}{2}t$  , where t is the time in minutes and v is the total volume in liters of water in the tank.

Graph 1

Graph 2

Task 2 Questions

• Answer the following questions and say which graph you used to find your answer.

• Q1: After 30 seconds, which tank has the most water? 

• Q2: At approximately what times do both tanks have the same amount of water? 

• Q3: At approximately what times do both tanks contain 1 liter of water? 20 liters? At approximately what times do both tanks contain 1 liter of water? 20 liters? 

Possible Responses

• A1: Using the first graph, Tank A has more water after 30 seconds.

• A2: Using the second graph, at approximately 64 minutes both tanks have the same amount of water.

• A3: Using the first graph, Tank A has a liter of water after 1 minute. Tank B has a liter of water after 2 minutes. Using the second graph, Tank A has 20 liters of water at around 36 minutes while Tank B has 20 liters of water at 40 minutes. Using the first graph, Tank A has a liter of water after 1 minute. Tank B has a liter of water after 2 minutes. Using the second graph, Tank A has 20 liters of water at around 36 minutes while Tank B has 20 liters of water at 40 minutes.

Poll

Cool Down: Which one of these relationships is different than the other three?

• Graph A

• Graph B

• Graph C

• Graph D

Possible Responses

Graphs A, C, and D are all representations of y= 5x. Graph B is a representation of y= 5.5x.