7.4.1-Explore Graphing Proportional Relationships

Multiple Choice

Which axis runs vertically?

• x
• Y

Multiple Choice

Which axis runs horizontally?

• x
• y

Multiple Choice

How do you write an ordered pair?

• (X,X)
• (Y,X)
• (X,Y)
• (Y,Y)

Multiple Choice

In the ordered pair (4,9) which number is the Y COORDINATE?

• 4
• 9
• neither
• both

Multiple Choice

Where is Point A on the coordinate plane?

• (7,4)
• (1,3)
• (9,3)
• (4,7)

Multiple Choice

The coordinates for the origin in the coordinate plane are________?

• (1,1)
• (0,0)
• (0,1)
• (1,0)

Multiple Choice

The two number lines are called the _______.

• origin
• axes
• quadrants
• coordinates

Multiple Choice

What is located at (5,3)?

• nothing
• point A
• the park
• point B

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

At what rate did the rain fall?

• 2 cm per hour
• ¹/₄ cm per hour
• ¹/₂ cm per hour
• 4 cm per hour

Multiple Choice

Which company shows a greater rate of change?

• Water's Edge Rafts
• Ryan's Rafts

​Look at the crosshairs.

​k = y/x

y = k(x)

Writing Equations (y = kx) from Graphs

• Look for the point where x = 1. This is the k value!! (unit rate)

• You can use any point (x,y) on the graph and divide y/x.

• Write the equation in the form y = kx.

Multiple Choice

Which equation represents the proportional graph?

(Click on the graph to make it bigger) 

• $$y\ =\ \frac{1}{2}x$$  

• y = 4x

• y = 2x

• $$y\ =\ \frac{1}{4}x$$  

Multiple Select

Select ALL of the graphs that could represent a proportional relationship.

​Constant of proportionality from graphs

​What are two different ways you can find a constant of proportionality using a graph?

1. ​Look at x=1 on the line to find what y equals...that is your constant.

2. ​Pick any clear point. Divide y by x.

Open Ended

What does the point (4, 60) on the graph represent?

Poll

What is the constant of proportionality?

• 15

• 1/15

• 20

• 1/20

Open Ended

If I wanted to know how many hours it would take Damon to bike 72 miles, what would I do?

Multiple Choice

How long would it take Damon to bike 72 miles?

• 5.8 hours

• 0.21 hours

• 4.8 hours

• 0.48 hours

Multiple Choice

What is the equation of this graph?

• y = kx

• y = 15x

• y = x/15

• y = k/x