Rates, Unit Rates, and Proportionality

Unit Rates and Proportional Relationships

7th Grade

Identifying Proportional Relationships in a Table

• Step 1: Form a ratio between each quantity in the table

• Step 2: Simplify each ratio

• Step 3: Compare the ratios and determine if the ratios are the same

• If the ratios are equivalent, the table represents a proportional relationship

Proportional Relationships on a Graph

If a straight line passes through the origin (0,0) on a graph, the relationship between y and x is a proportional relationship.

Constant of Proportionality

Remember: The constant of proportionality is the value the equivalent ratios have in common in a proportional relationship.

To represent a proportional relationship using an equation, we use the equation y=kx where k represents the constant of proportionality.

Let's Practice

• Represent the relationship in a table

• Identify whether the relationship between number of cups and pounds of sugar is proportional.

• Find the constant of proportionality

• Represent the relationship using an equation

Multiple Choice

Did the table represent a proportional relationship?

• No

• Yes

Open Ended

What equation would represent the proportional relationship in question 12 and 13?

Multiple Choice

Does the graph represent a proportional relationship?

• yes

• no

Multiple Choice

Which equation represents the proportional relationship? 

• y=0.5x

• y=1.5x