Proportional Relationships

PROPORTIONAL RELATIONSHIPS

What are proportional relationships?

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other.

​The numbers in the table represent a proportional relationship because each value for the "Number of portraits" is being multiplied by the same constant (5) to get the "Time".

​Drew is an artist. He paints portraits. The table below shows the number of portraits painted in hours. Do the numbers in the table represent a proportional relationship?

​Proportional Tables

Multiple Choice

This table shows the amount earned by Harry for selling cups of ice cream. Do the numbers in the table represent a proportional relationship?

• Yes

• No

Multiple Choice

Daisy made an envelope from sheets of paper. The table below shows the number of envelopes made by the number of sheets. Do the numbers in the table represent a proportional relationship?

• Yes

• No

Multiple Choice

Fred wrote notes during an examination. The table below shows number of pages written in relation to the time it took to make the notes (in hours). Does the table represent a proportional relationship?

• Yes

• No

Multiple Choice

Verda used a sensor to measure the speed of a moving car at different times. At each time, the sensor measured the speed of the car in both miles per hour and kilometers per hour. The table shows her results.

Based on her results, which statement describes the relationship between m, the speed of the car in miles per hour, and k, the speed of the car ni kilometers per hour?

• The relationship is proportional because the ratio of m to k is constant.

• The relationship is not proportional because the ratio of m to k si constant.

• The relationship is proportional because the difference between m and k si constant.

• The relationship is not proportional because the difference between m and k is constant.

The constant of proportionality is a fixed number that indicates the rate at which ratios increase or decrease.

Constant of Proportionality

Graphs of proportions have a straight line that passes through the origin (0,0)

How to recognize

Proportional Graphs

​The constant of proportionality is 10 because each "x" value is multiplied by 10 to get the "y" value.

The point (2, 20) represents the fact that if you have 2 seed packets you will get 20 plants.

The graph below represents the total number of plants and number of seed packets used.
a) What is the constant of proportionality?
b) What does the point (2, 20) represent?

​Proportional Graphs

Multiple Choice

The graph represents the total number of cups of coffee and the total amount of sugar required to make the coffee. What is the constant of proportionality?

• 4

• 60

• 5

• Not enough information is provided

Multiple Choice

The graph represents the number of pieces of paper that are found in boxes. What is the constant of proportionality?

• 46

• 20

• 7.5

• 12.5

Within

Solving Proportions
(3 Ways)

Between

Cross Product

Multiple Choice

Which of the following pairs of ratios does NOT form a proportion?

Multiple Choice

Which group contains ratios that are all equivalent to 3/5 ?

Fill in the Blanks

Find the value of x for the pair of similar triangles

Fill in the Blanks

Find the value of y for the pair of similar triangles

Fill in the Blanks

Find the value of x in the pair of similar triangles

Fill in the Blanks

Find the value of y in the pair of similar triangles