CHAPTER 4

EQ: How do I determine a proportional relationship?

PROPORTIONAL VS. NON-PROPORTIONAL

If two quantities are proportional, then they have a constant ratio.

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

VOCABULARY

Proportional: For a relationship to be constant there has to be a constant ratio. The graph of a proportional relationship will cross through the origin (0,0)

Nonproportional: No constant ratio. The graph will not cross the origin.

IS IT PROPORTIONAL?

Uptown pizzeria sells medium pizzas for $7 each .Is the cost of an order proportional to the number of pizzas ordered?

Find the cost for 1,2,3,and 4 pizzas and make a table to display numbers and cost.

PROPORTIONAL RELATIONSHIPS

Will always go through the origin on a graph. (0,0)

Graph will always be a straight line. Always write the constant ratio in the

form of

Reduce or divide to find the constant ratio for each.

y

x

In order to tell if a graph is proportional the line must go through the origin.

EX 3. and 4.) Tell if the following graphs represent a proportional relationships.

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

USING A TABLE TO DETERMINE A PROPORTIONAL RELATIONSHIP

The example below shows the distance Keisha traveled during a bike-a-thon. Is there a proportional relationship between time and distance?

The ratios are equivalent, so there is a proportional relationship between time and distance.

USING A GRAPH TO FIND A UNIT RATE

PROPORTIONAL OR NON-PROPORTIONAL?

In order to tell from a table if there is a proportional relationship or not, you can check to see if the ratio is the same.

The ratio is also known as the scale factor.

y

x

y

x

EX 1. and 2.) Tell if the following tables represent a proportional relationships.

y

xx y

5 10

8 16

10 20

14 28

21 42

Proportional? ______ Ratio _________

EQUATIONS:

We will also make equations to describe each situation.

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

Make sure you define your variables!!!

Write an equation that fits this situation: Hint: Use your constant ratio!!

4

x cupsof lemon juice

y cupsof water

x y

Ex. 2) A lemonade recipe calls for 1.5 cups of lemon juice and 6 cups of cold water.

Lemon Juice

Cups of Water

1.5 6

3 12

4.5 18

6 24

DRAW THE GRAPH OF THE TABLE BELOW

Cups of WaterLemon Juice

Cups of Water

1.5 6

3 12

4.5 18

6 24

EXAMPLE 1 IDENTIFY PROPORTIONAL RELATIONSHIPS

Sal’s Pizzeria sells large pizzas for $11 but charges a $2 delivery fee per order.

Write an equation to fit this situation:

11 2

x numberof pizzas sold

y Total Cost

x y