Proportional Relationships from Tables & Graphs

​x
y

Fill in the Blanks

Fill in the Blanks

TABLES. Proportional or Not?

Determine the constant of proportionality.

Then state if the data table has a proportional relationship. 

TABLES. Proportional or Not?

Determine the constant of proportionality.

k=12 for each x and y.

Then state if the data table has a proportional relationship. Yes, y/x stays the same.

Fill in the Blanks

TABLES. Proportional or Not?

Determine the constant of proportionality.

Then state if the data table has a proportional relationship. 

TABLES. Proportional or Not?

Determine the constant of proportionality.

k= 0.50 for each x and y.

Then state if the data table has a proportional relationship. Yes, y/x stays the same

Multiple Choice

Does the following table show a proportional relationship?

• Yes

• No

TABLES. Proportional or Not?

Determine the constant of proportionality.

Then state if the data table has a proportional relationship. 

TABLES. Proportional or Not?

Determine the constant of proportionality.

k=7.33, 4, 2.77, 2.25

Then state if the data table has a proportional relationship.  No, y/x does not remain the same

Proportional vs. Non-Proportional from a Graph

Multiple Select

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

Does this graph show a proportional relationship?

• Proportional graphs have points that create straight lines

• Proportional graphs go through the origin or (0,0)

Multiple Choice

Which graph shows a proportional relationship?

• A

• B

• C

• D

Is this proportional?

To solve, check each ordered pair for a rate of change.
10/1 = 10
20/2 = 10
70/7 = 10
100/10 = 10
Yes, the rates are constant, so this is proportional.

Is this proportional

Check all the rates of change.

-10/70 = -1/7

-9/63 = -1/7

-5/35 = -1/7

-3/21 = -1/7

All of the rates of change are constant (-1/7), so this is proportional. 

Open Ended

Does this graph represent a proportional relationship? Explain why or why not.

Multiple Choice

Does the table below represent a proportional relationship? Explain why or why not

• Yes

• No

• Yes, the constant of proportionality is the same

• No, the constant of proportionality is not the same

Multiple Choice

This pair of ratios forms a proportion: $$\frac{8}{5}$$ and $$\frac{b}{35}$$ what would b have to be?

• 40

• 7

• 18

• 56

Multiple Choice

Does this table represent a proportional relationship? If so, what is the constant of proportionality.

• Yes, 6

• Yes, 5

• Yes, 5

• No

Multiple Choice

Does this graph represent a proportional relationship? Explain why or why not.

• Yes, is a straight line

• Yes, passes through the origin

• No, doesn't start at the origin

• No, line is curved

Multiple Choice

Fill in the missing values for the proportional relationship.

• 0, 6, 55

• 0, 7, 55

• 6, 55, 100

• 8, 12, 13

Proportional Relationships with Graphs

EQ: How can you use graphs to represent and analyze proportional relationships?

Page 10

Fill in the Blanks

Open Ended

What do you notice about the graph?

(Click on the graph to enlarge the image.)

Graphing Proportional Relationships

Objective: Describe how proportional relationships are represented using the coordinate plane

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 (0,0)

• It makes a curved line.

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

What Could the Graph Represent?

Here is a graph that represents a proportional relationship.

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

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

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

• y
• x
• 14
• y=14

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

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.

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

Poll

Did you watch the lesson video before class?

• Yes,

• No.

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

Does the image show a proportional relationship? (Yes or No)

• Yes (straight line and through the origin)

• No, straight but not through the origin.

• No, through the origin but not straight.

• No, not a straight line or through the origin.

Get out your notes.

Turn to page 10.

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

Open Ended

Why does a line passing through (0, 1) NOT show a proportional relationship?

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

Open Ended

Look at the "Your Questions" column of your notes. Write any questions you wrote down. If no questions, tell me how well you think you understand this material/lesson.

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.

Assignment/Asynchronous Time/Homework:

Assignment: Week 7 Assignment #1-5 only!

Homework: No video to watch. Catch up on missing work/finish Unit 1 Test.

Come to homeroom or sign up for a wednesday appointment if you need help with any of your math! I can't help if you don't ask!

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).