Interpret Graphs of Proportional Relationships

Proportional Relationships:

Reading Graphs

By Ms. Rush

What do you know???

Multiple Choice

An ordered pair is written in the form ...

• (x, y)

• (y, x)

• (a, b)

• (0, 0)

Multiple Choice

Ordered pair (0,0) is also known as the ___.

• y-axis

• x-axis

• origin

• constant

Multiple Choice

What makes a graph proportional?

• Straight Line
• The line goes through (0,0)
• Curvy line
• Straight line and passes through (0,0)

Multiple Select

Which graphs below represent proportional relationships?

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).

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).

This is an example of a graph with a line that is proportional. The constant of proportionality is 5. You can find the constant of proportionality by dividing one of the time values by the water values.

This is another example of a proportional relationship on a graph. The line goes through the origin (0, 0) and is a straight line. The constant of proportionality would be 50. In the context of the problem it takes 1 hour to get a total cost of $50.

This is an example of a non proportional relationship. In this situation, the line is a straight line, however the line does not cross the origin (0, 0).

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

Multiple Choice

Divide $$\frac{y}{x}$$   to find the constant of proportionality.

• 2

• 3

• 4

• 9

Multiple Choice

Divide $$\frac{y}{x}$$   to find the constant of proportionality.

• 5

• 3

• 6

• 30

Multiple Choice

Divide $$\frac{y}{x}$$   to find the constant of proportionality.

• 5

• 25

• 4

• 10

Multiple Choice

Divide $$\frac{y}{x}$$   to find the constant of proportionality.

• 12

• 7

• 4

• 28

Multiple Choice

Divide $$\frac{y}{x}$$   to find the constant of proportionality.

• 5

• 9

• 10

• 45

Multiple Choice

Divide $$\frac{y}{x}$$   to find the constant of proportionality.

• 21

• 3

• 14

• 7

Identifying Unit Rate and K from a Graph

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