Proportional Relationships

Categorize

Options (4)

WARM UP: Organize these options into the right categories

Proportional

Not Proportional

Categorize

Options (6)

$$y=10x$$  

$$y=\frac{5}{3}x$$  

$$y=3x+4$$  

$$y=-9x$$  

$$y=3.2x$$  

$$y=4x-7$$  

WARM UP: Organize these options into the right categories

PROPORTIONAL

NOT PROPORTIONAL

• Read the labels for the x and y axis.

• X is at the bottom, Y is on the side.

• All points have an (x, y)

• There are 4 jam jars for every 2 cups of sugar.

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​Some text here about the topic of discussion.

​What does the point (4,2) mean?

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Characteristics of Proportional Graphs.

• They are in the shape of a straight line.

• They start or cross at the point of origin.

Multiple Choice

What does the point (6, 4) mean on the graph?

• 6 laps in 4 minutes

• 2 laps in 3 minutes

• 2/3 of a lap in 1 minute

• 4 laps in 6 minutes

Multiple Choice

What does the point (2, 94) represent in this situation?

• Every week, they earn $94.
• After 94 weeks, they save $2.
• After 1 week, they save $47.
• After 2 weeks, they save $94.

Multiple Choice

What does the ordered pair (20, 3000) represent?

• The machine folds 3,000 sheets in 20 minutes.
• The machine folds 20 sheets in 3,000 minutes.
• There are 3,000 sheets in 20 minutes.
• There are 20 sheets in 3,000 minutes.

Open Ended

Constant of Proportionality (Unit Rate)

How do you find the unit rate on a graph?

1. 1. Pick a point on the graph

2. 2. Divide $$\frac{y}{x}$$

Multiple Choice

What is the unit rate/constant of proportionality?

• 80 miles in 1 hours

• 20 miles in 1 hours

• 40 miles in 1 hours

• 160 miles in 1 hours

Multiple Choice

What is the constant of proportionality (unit rate) of the speed of the sloth based on the graph?

(Click the graph to enlarge the image.)

• 1 minute per 6 feet

• 6 feet per minute

• 1 minute per 3 feet

• 3 feet per minute

Multiple Choice

Find the constant rate of change for this graph.

• 2 lb per person

• 1 lb per person

• 3 lb per person

• 4 lb per person

-Find a point on the graph.

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-Divide y/x to find the constant.​

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-Create an equation. y = kx​

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Write an equation for the graph.

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Multiple Choice

Which equation matches the graph?

• y = 7x
• y = 42x
• y = 6x
• y = 2x

Multiple Choice

Create an equation for this proportional relationship. 

• y = 10x
• y = 5x
• k = 5
• y = 0.5x

Multiple Choice

Which equation would be use to create the graph above?

• y = 50x

• y = 2x

• y = 0.02x

• 
  

  $$y\ =\frac{1}{50}x$$
  

-Find a point on the graph.

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-Set up a proportion.

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How many gallons of water would you have after 10 minutes?

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Multiple Choice

Based on the graph, how much would it cost to rent a limo for 15 hours?

• $1500

• $750

• $500

• $1000

Multiple Choice

Use the graph to determine how much 9 lbs of chicken salad costs?

• $67.50

• $60

• $75

• $52.50

Multiple Choice

Based on the graph, how many miles were traveled after 8 hours?

• 400

• 800

• 600

• 
  

  300