xxxxx 6x=(5)8.40 X = 7 liters

Warm -up

At a local college, the ratio of girls to boys is 3:5. If there are 2700 girls, how many boys are there?

4500

PROPORTIONAL VS. NON-PROPORTIONALTuesday, April 11, 2023

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 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.

y

x

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.

y

x

y

x

Determine if the tables below represent a proportional relationship.

y

x

Number of books

(x)

Price (y)

1 3

3 9

4 12

7 18

y

x

Pounds (x)

Cost (y)

4 $1

6$1.5

0

8 $2

10$2.5

0

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

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

In order to tell if a set of ordered pairs is proportional, look at the ratio of y to x.

Does the following set of ordered pairs represent a proportional relationship?

8, 4 , 10, 5 , 5, 2.5 , 12, 6

Proportional? ________

Ratio __________

Equation ___________

Constant of proportionality _______

PROPORTIONAL RELATIONSHIPS: ORDERED PAIRS

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

At HMS, there is an average of 26 students per teacher. Complete the table below to show the proportional relationship.

Teachers

1 5 10 25

Students 26

The City Pool costs $8 per day to visit during the summer. There is also a $25 yearly registration fee.

Complete the table below. Write an equation for the relationship where C

equals total cost and d equals daily cost. Is the total cost proportional to the total number

of days visited? Explain why or why not.

Day 1 2 5 10

Cost 33

IDENTIFY PROPORTIONAL RELATIONSHIPS

Ex. 1: Sal’s Pizzeria sells large pizzas for $11 but charges a $2 delivery fee per

order.

Create a table that shows the cost for 1, 2, 3, and 4 pizzas.Create a graph to demonstrate this relationship.Write an equation to fit this situation.Is this a proportional relationship?

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

Complete the table and create a graph. Write an equation that fits this situation.

(Hint: Use your constant of proportionality!!)

Ex. 2: Your dad is making trail mix. Determine if the quantities of nuts and fruit are proportional for each serving size shown in the table below.

Cups of nuts

(x)

Cups of fruit (y)

yx

Unit Rate

1.5 6

3 12

4.5 18

6 24

HOMEWORK

FUNction graFUN worksheet

Word problems

Ashley and Megan are running around a track. They run equally fast, but Ashley started later. When Ashley has run 5 laps, Megan has run 15 laps. When Ashley has run 30 laps, how many laps has Megan run?

Aunt Jo put 3 towels on the clothesline and Sue put 6. All of the towels are identical in terms of size, thickness, etc. It took 12 hours for Aunt Jo’s towels to dry. How long did it take Sue’s towels to dry?

Solve the following problems. Are they proportional or non-proportional?

Harris Teeter has bags of apples on sale! Each bag contains the same number of apples. Your mom buys 2 bags and gets a total of 16 apples. Your grandmother buys 10 bags. How many apples did she get?

John owns a bakery. His recipe calls for 10 ounces of flour to make a pound of bread. How much bread will he make if he uses 23 ounces of flour?

The locomotive of a train is 12 meters long. If there are 4 carriages connected to the locomotive, the train is 52 meters long. If there were 8 carriages connected to the locomotive, how long would the train be?

A group of 5 musicians plays a piece of music in 10 minutes. Another group of 35 musicians will play the same piece. How long will it take this group to play?

Yesterday, a boat carrying 326 Toyota Corollas arrived in port. The total weight of the cars was 521 tons. Tomorrow, another boat will arrive into port carrying 732 Corollas. What will be the total weight of the cars?