Proportional Relationships: Graphs

Proportional Relationships: 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

Does the graph represent a proportional relationship?

• yes
• no

Multiple Choice

Does the graph represent a proportional relationship?

• yes
• no

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 Choice

Josh bought a pizza with 8 slices of pizza for $12. What is the cost of a slice of pizza?

• $12

• $1.50

• $20

• $1

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y
• x
• 14
• y=14

Poll

How did you do?

• I got every answer correct.

• I knew some of the answers.

• I got everything wrong.

Characteristics of Proportional Graphs.

• They are in the shape of a straight line.

• They start or cross at the point of origin.

This is the graph that is proportional.

Because the line is linear (straight line) and passes through the origin (0,0).

Multiple Choice

Which graph is 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

Multiple Choice

Does this graph represent a proportional relationship?

• Yes - Proportional

• No - Not Proportional

Proportional vs. Non-Proportional from a Graph

Multiple Select

Choose the graph(s) that DO NOT represent proportional relationships.

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

Calculating Unit Rate from a Proportional Graph

We can use individual points on the line to calculate the unit rate...

We just need to remember to create a ratio and divide.

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

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

What is the unit rate for the rain fall?

(Click on the graph to enlarge the image.)

• 2 cm per hour

• 1 cm per hour

• ¹/₂ cm per hour

• 4 cm per hour

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 Choice

The following graph is not proportional, why is that?

(Click the graph to enlarge the image.)

• We don't know what number it starts at.

• It does not pass through the origin.

• But it IS proportional!

Multiple Choice

What makes a graph between two quantities proportional?

• It makes a straight line.

• The line goes through the origin (0,0)

• It makes a curved line.

• It makes a straight line and passes through the origin (0,0).

Poll

Do you think you can tell the difference between a proportional graph and a nonproportional graph?

• Yes

• No