Graphing Proportional Relationships

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

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

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 graph represents the number of words Taylor can type over a certain number of minutes. Which of the following statements is true?

(Click the graph to enlarge the image.)

• Taylor can write 6 words per minute

• Taylor can write 25 words per minute

• Taylor can write 50 words per minute

• Taylor can write 150 words per minute

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

You travel 150 miles on 5 gallons. What is the unit rate in miles per gallon?

• 15 miles per gallon

• 30 miles per gallon

• 3 miles per gallon

• 25 miles per gallon

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

What makes a graph between two quantities proportional?

• It makes a straight line.

• The line goes through (0,0)

• It makes a curved line.

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