PROPORTIONAL VS. NON-PROPORTIONALThursday, May 4, 2023

REVIEW KEY VOCABULARY Proportional – when two quantities that simplify

to the same ratio.

Constant – a quantity having a value that does not change or vary.

Constant of Proportionality - a constant value of the ratio of two proportional quantities.

PROPORTIONALITY Two quantities are directly proportional

if they have a constant ratio .

The change in one variable is always accompanied by a change in the other.

This constant ratio is called the “constant of proportionality”. The constant of proportionality can never be zero.

PROPORTIONAL RELATIONSHIPSIdentify the constant of proportionality:

The constant of proportionality is the unit rate From the table, look at the ratio of y to x From the graph, look at the steepness of the graph or

look for the y-value where x is one From the equation, look for the coefficient of x

PROPORTIONAL VS. NON-PROPORTIONAL Two quantities are directly proportional

if they have a constant ratio .

If the ratio is not constant, the two quantities are non-proportional.

We will look at tables, graphs, equations, and ordered pairs to determine if the relationship between the variables is proportional.

yx

EQUATIONS: You should also be able to write equations to

describe the relationships.

If the situation is proportional, you will use your constant of proportionality in your equation.

Be sure to define your variables!!!

PROPORTIONAL RELATIONSHIPS: TABLES In order to tell from a table if there is a

proportional relationship between the variables, you should check to see if the ratio is the same for all values in the table.

The ratio is also known as the scale factor.

Reduce or divide to find the constant of proportionality (unit rate) that defines the relationship between the variables.

yx

yx

Determine if the tables below represent a proportional relationship.

yx

Number of books

(x)

Price (y)

1 3

3 9

4 12

7 18

yx

Pounds (x)

Cost (y)

4 $1

6 $1.50

8 $2

10 $2.50

Proportional? ________

Ratio __________

Equation ___________

Const of Prop __________

Proportional? ________

Ratio __________

Equation ___________

Const of Prop __________

Proportional? ________

Ratio __________

Equation ___________

Const of Prop __________

Proportional? ________

Ratio __________

Equation ___________

Const of Prop __________

Proportional? ________

Ratio __________

Equation ___________

Const of Prop __________

PROPORTIONAL RELATIONSHIPS: GRAPHS The graph of a proportion will always

be a straight line that passes through the origin (0,0).

Always write the constant ratio in the form of .y

x

A Common Mistake

Graph of a Proportional Relationship:

Determine if the graphs below represent a proportional relationship.

1 2 3 4 5

1

2

3

4

5

x

y

1 2 3 4 5

1

2

3

4

5

x

y

Proportional? _________

Proportional? _________Why? Line goes thru the origin

Why? Line does notgo thru the origin

Core Lesson

What is the constant of proportionality?

(0,0)(1,45)

(2,90)(3,135)

(4,180)

Core Lesson

(0,0)(1,45)

(2,90)(3,135)

(4,180)

451

902

1353

1804

yx

Proportional? How can You determine the unit rate from a graph?Constant of proportionality?

Equation?

Proportional? How can You determine the unit rate from a graph?Constant of proportionality?

Equation?

Proportional? How can You determine the unit rate from a graph?Constant of proportionality?

Equation?

Determine if the following equations show a proportional relationship.

Substitute a zero for x in the equation and then solve. If y then equals zero, then the equation represents a

proportional relationship because the graph of the line goes through the origin.

y = 3x – 1 y = 10x

PROPORTIONAL RELATIONSHIPS: EQUATIONS