STUDY Guide: Proportional Reasoning

Proportional Relationships

​

What you need to know​

​A proportional relationship is based on equivalent ratios

Or multiplicative relationships only.... no adding or subtracting or exponent or square root steps... just multipliccaiton.

Ask yourself...

If I start with x and end with y, what did I multiply x by?

Does it look like I need to divide to get from x to y? If so, what would that look like as multiplication?

What if I work backwards and do the y values divided by the x values?

Characteristics of Proportional Graphs.

• They are always graphed as a straight line.

• They start at or cross through the origin

  • Graphs of proportional relationships must contain (0,0) since any number times zero is zero​

Characteristics of Non-Proportional Graphs.

• A graph is non-proportional if it meets ANY of these:

  • It isn't a straight line (bottom picture)

  • It doesn't go through the origin (top picture)

How to tell if a Graph is Proportional?

Multiple Choice

The origin is located where in the coordinate plane?

• (0, 0)

• (10,10)

• (100, 100)

• (50, 50)

Multiple Choice

Does this graph represent a proportional relationship?

• Yes
• No

Multiple Choice

Is the graph proportional or non proportional?

• proportional
• non proportional

Constant of Proportionality in a Table​

• Represented by k

• The way to find k, the constant of proportionality, is to do y/x

• It is the same unit rate or "how much per one" you calculated in 6th grade 

• It is the multiplicative rule or relationship from one unit to the next.

• THE TABLE MUST HAVE A CONSTANT OF PROPORTIONALITY TO BE PROPORTIONAL.​

​y/x

1/2 = 0.5

2/4 = 0.5

3/6 = 0.5

4/8 = 0.5

5/10 =0.5

The table is proportional​

​Constant of Proportionality from a table?

Must Divide: ** y ➗​ x **

Multiple Choice

What does the point (2, 94) represent in this situation?

• Every week, they earn $94.
• After 94 weeks, they save $2.
• After 1 week, they save $47.
• After 2 weeks, they save $94.

Multiple Choice

What does the ordered pair (20, 3000) represent?

• The machine folds 3,000 sheets in 20 minutes.
• The machine folds 20 sheets in 3,000 minutes.
• There are 3,000 sheets in 20 minutes.
• There are 20 sheets in 3,000 minutes.

Multiple Choice

What is the constant of proportionality?

• 15
• 5
• 75
• 25

Multiple Choice

Does the table represent a proportional relationship?

• Yes.
• No.

Multiple Choice

What is the constant of proportionality?

• $3
• $4
• $2
• $9

Math Response

Based on the information in the table, what is the constant of proportionality?

Type answer here

Correct Answer: \frac{1}{2}

Deg^°

Rad

Math Response

Based on the information in the table, what is the constant of proportionality?

Type answer here

Correct Answer: 3

Deg^°

Rad

Proportional Equations

​​y = k x

where "k" is the constant of proportionality​

​y = 3x

​3 is the C.O.P.

Constant of Proportionality 

​To write an equation, find the multiplicative rule...

Some text here about the topic of discussion

​​x = number of items

y = cost​

​

y = kx and k = 5​

y = 5x

Is the equation​​

​k = y/x

​ = 5/1 = 5

​ = 25/5 = 5

​ = 50/10 = 5

​ = 250/50 = 5

k = 5​

​x

y​

Multiple Choice

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

• y
• x
• 14
• y=14

Multiple Choice

Identify the constant of proportionality.

• k = 2x

• k = 2

• k = 4

• none (not proportional)

Multiple Choice

Write the equation for the table given

• y = 1/3x
• y = 3x
• y = 1/2x

Multiple Choice

Write the equation for the table given.

• y = 16/2x
• y=8x
• y=12x

Fill in the Blanks

What is the constant of proportionality in the equation?

$y=3x$  

k=

Multiple Choice

Write an equation for this relationship.

• y=1/5x
• y=1/2x
• y=2x
• y=5x

Find the constant of Proportionality from a graph

How do we find the COP from a graph?

Math Response

What is the constant of proportionality of the graph?

k=

Type answer here

Correct Answer: 2

Deg^°

Rad

Multiple Choice

What is the constant of proportionality of the graph?

k=

• 2/3
• 3/2

• 2

• 3

Multiple Choice

What is the constant of proportionality for the following graph?

• 80
• 20
• 40
• 160

Multiple Choice

Identify the constant of proportionality.

• k = 20

• k = 1/5

• k = 1

• k = 2.5

• none (not proportional)

Multiple Choice

What is the constant of proportionality? 

• 4
• 1/4
• 8
• 1/8

Multiple Choice

Who swims their laps faster?

click on the photo to enlarge!

point on graph (4, 9)

• Natalie

• Mary Claire

Multiple Choice

Phil ran 20 laps in 30 minutes. James time is represented on the graph. What is the pace of the fastest runner?

• 1.5 minutes/lap

• 3 minutes/lap

• 1.5 laps/minute

• 3 laps/minute

Multiple Choice

Sebastian's workout burn's calories at the rate y=15x. Julio's calorie burn is on the table. How many MORE calories are burned by the person who burns the most?

• 1

• 2

• 0.5

• 1.5

Multiple Choice

How does the speed of a sloth compare to the speed of the Mars Rover?

• A sloth is faster than the Mars Rover.

• A sloth is slower than the Mars Rover.

• A sloth goes the same speed as the Mars Rover.

• This is not enough information.