Proportional or Nonproportional?

How can I show proportion?

Definition

Proportional -A relationship is proportional if one quantity is a multiple of others.

Multiple - that number multiplied by an integer. Example: Multiples of 3 include 3, 6, 9, 12, 15, 18, etc.

Showing Proportion in Multiple Ways

Table: Equivalent ratios of y/x can be seen in a table.

Graph: A straight line through the origin.

Equation: An equation of the form y = kx where k is the constant of proportionality.

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Example of a Proportional Relationship

Three pounds of chicken cost $6. What is the cost of x pounds of chicken?

Equation: y= 6/3x OR y=2x

Table: Graph:

If x=2 then y=

4/2 =

If x= 4 then y=

8/4 =

Now What?

If the ratios are equivalent then the relationship is proportional.

With the graph, the origin is 0,0 (the starting point). A straight line through the origin = proportional.

The relationship between the pounds and cost is

proportional. The table has equivalent ratios (2/1=4/2=6/3),

the graph is a straight line through the origin, and the

equation is of the form y=kx (y=2x).

Non-Proportional

A relationship is not proportional is the table does not have an equivalent ratio y/x or an equation of y=kx.

Cues to Remember:

• The table does not contain equivalent ratios.
• The graph does not pass through the origin.
• The equation contains addition or subtraction.

Non-Proportional Examples

The county fair cost $5.00 to enter and $1.00 per ride.

Equation: y = x + 5

Table:

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The relationship between the rides and cost is not proportional.

Summary

• I can see proportion with tables, equations, and graphs.
• Tables show proportion when an equivalent ratio is shown.
• Graphs show proportion when a straight line goes through the origin.
• Equations show proportion when there is a constant change with y=kx.

constant