Math 8 Proportional Relationships for 11/3

Graphing Proportional Relationships

Objective: Describe how proportional relationships are represented using the coordinate plane

Open Ended

What do you notice about the graph?

(Click on the graph to enlarge the image.)

Properties of Proportional Graphs

• All graphs of proportional relationships are represented with a straight line to show a constant rate also known as LINEAR.

• All proportional relationships pass through the origin.

• Can be used to calculate the unit rate or constant of proportionality.

Multiple Choice

The graph represents the number of laps a car drove around a track compared to the number of minutes.

How many laps did the car do in 6 minutes?

(Click the graph to enlarge the image.)

• 2 laps

• 6 laps

• 4 laps

• 9 laps

Multiple Choice

The graph above shows the price of games in dollars. Is the graph proportional and how do you know?

(Click the graph to enlarge the picture.)

• The graph is proportional because it is a straight line.

• The graph is proportional because it is a straight line that passes through the origin.

• The graph is not proportional because it does not pass through the origin.

• The graph is not proportional because it is not a straight line and it does not pass through the origin.

Multiple Select

Which of the following graphs demonstrates a non-proportional relationship? (Select ALL that apply)

Multiple Choice

• a

• b

• c

• d

Multiple Select

What qualities must a graph have in order for it to be proportional? (Select ALL that apply)

• Must cross through the Origin, point (0,0)

• Must always be positive

• Must be a line

• Must be a straight line; has to be linear

Multiple Choice

What is the unit rate in miles per hour for this proportional relationship?

(Click the graph to enlarge the image.)

• 60 miles per hour

• 120 miles per 2 hours

• 1 mile per hour

• 60 miles per 2 hours

Draw

Which letter choice represents the equation for the word problem?

Multiple Choice

Read the question and choose the right equation that represent the situation.

• a

• b

• c

• d

Draw

Complete #4 and #5. For each quetions, select the right equation that represents the word problem.

Multiple Choice

Which graph is proportional?

• A
• B
• C and D
• All of the graphs are proportional

Multiple Choice

Which graph is non-proportional?

• A
• B
• C
• D

Draw

Find the slope. You can use rise/run to calculate the slope. You may draw on the graph. Write your answer as a fraction.

Match

Match the following proportional situations to their slope. m represents the slope.

• There are 6 fights in 3 days. What slope could represent the amount of fights each day.

• A swimmer swims 26 lapes each minute. What slope could represent this situation?

• 20 pieces of velcro are needed to hang up 5 posters. What slope could represent the unit rate for pieces of velcro per poster?

• 240 bricks, y, are needed to build 2 walls, x. Which slope best represents this relationship?

m=2

m=26

m=4

m=120

• m=2

• m=26

• m=4

• m=120

Graphing

A store sells 2 bags of chips for $5. Using this information, how much is it for 4 bags of chips? Identify two points and graph this scenario on the coordinate plane.

Let x represent the number of bags and let y represent the dollar amount.

Multiple Choice

What does the point (1, 50) represent in the graph?

• Each (1) bag of rice has 50 varieties of rice

• Each (1) bag of rice weighs 50 pounds

• Each (1) bag of rice costs $50

• Each (1) bag of rice has 50 different colors of rice

Multiple Choice

Is this graph proportional?

• No, it passes through the origin

• No, it is a single straight line

• Yes, it passes through the origin and is a single straight line

Multiple Choice

Which equation matches the graph?

• y = 60x
• y = 40x
• y = 80x
• y = 20x

Multiple Choice

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

• $8 per pound

• $35 per pound

• $5 per pound

• $0.125 per pound