Proportional Relationships with Graphs

Graphing Proportional Relationships

- I can identify a proportional relationship from a graph.

- I can identify the unit rate (1,r) from a graph.

Properties of Proportional Graphs

• All graphs that represent a proportional relationship must be a straight line (linear)

• Proportional relationships must also show the line passing through the origin (0,0)

• The point on the graph (1, r) is the unit rate which is also constant of proportionality (k).

Multiple Choice

Does this graph represent a proportional relationship?

• Yes - Proportional

• No - Not Proportional

Multiple Choice

Does this graph represent a proportional relationship?

• Yes - Proportional

• No - Not Proportional

Multiple Choice

Does this graph represent a proportional relationship?

• Yes - Proportional

• No - Not Proportional

Multiple Choice

Does this graph represent a proportional relationship?

• Yes - Proportional

• No - Not Proportional

Multiple Choice

Does this graph represent a proportional relationship?

• Yes - Proportional

• No - Not Proportional

Identifying Unit Rate and K from a Graph

• The point on the graph (1, r), where r represents the unit rate, is also constant of proportionality (k).

Multiple Choice

What is the unit rate (or "k") in this graph?

• 24

• 32

• 34

• 36

Multiple Choice

What is the unit rate (or "k") in this graph?

• 24

• 32

• 34

• 12

Multiple Choice

What is the unit rate (or "k") in this graph?

• 10

• 15

• 30

• 35

Multiple Choice

What is the unit rate (or "k") in this graph?

• 20

• 40

• 60

• 80

Identifying Unit Rate and K from a Graph

• So what happens when you don't see (1, r) plotted on the graph?? ...

• Coordinate pairs can also be used to calculate the unit rate because k is the same thing as unit rate!

   $k=\frac{y}{x}$  where y is the y-coordinate and x is the x-coordinate.

Multiple Choice

What is the unit rate (or "k") in this graph?

• 2

• 4

• 6

• 8

Multiple Choice

What is the unit rate (or "k") in this graph?

• 2

• 4

• 5

• 10

Describing the Meaning of Unit Rate from a Graph

• Unit rate and the constant of proportionality describe the relationship between two quantities.

• This graph shows k=10/5 so k=2.

• The graph shows, for every 1 text message sent, we are charged $2.00!

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

What does the point (1, 60) represent in the graph?

• It takes 60 minutes to go 1 mile

• Every 60 minutes the family take 1 break

• In (1) one hour, the family travels 60 miles

• The family travels (1) one mile in (1) one hour

Multiple Choice

What does the point (1, 7.5) represent in the graph?

• Every (1) pound of chicken salad costs $7.50

• For every $7.50 spent, I get some chicken salad

• 7.5 chickens are used in each batch of chicken salad