PROPORTIONAL VS. NON-PROPORTIONAL Tuesday, April 11, 2023

PROPORTIONAL VS. NON-PROPORTIONAL Tuesday, April 11, 2023

PROPORTIONAL VS. NONPROPORTIONAL If two quantities are proportional, then they have a constant ratio. If the ratio is not constant, the two quantities are said to be nonproportional. We will make tables and look at the relationship between the variables to determine proportionality.

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 y x Reduce or divide to find the constant ratio for each.

PROPORTIONAL OR NONPROPORTIONAL? In order to tell from a table if there is a proportional relationship or not, you can check to see if the ratio y is the same. x The ratio factor. y x is also known as the scale

EX 1. and 2.) Tell if the following tables represent a proportional relationships. x y 5 10 8 16 10 20 14 28 21 42 y x Proportional? Ratio Equation Ordered Pair x y 0 2 3 8 5 12 9 20 10 22 y x Proportional? Ratio Ordered Pair

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. y y 5 5 4 4 3 3 2 2 1 1 x 1 x 1 2 3 4 3 4 5 5 Proportional ? Why? 2 Line goes thru the origin Proportional ? Why? Line does not go thru the origin

In order to tell if a set of ordered pairs is proportional, look at the ratio of y to x. EX 5.) Tell if the following set of ordered pairs represents a proportional relationship. 8, 4 , 10, 5 , 5, Proportional? Ratio 2.5 , 12, 6 Equation Ordered Pair

EX 6. and 7.) Determine if the following equations show a proportional relationship. Put a zero in for x; if y is zero then it is a proportional relationship because it goes through the origin. y 3x – 1 y 10x

8. At HPMS, there are 26 students per teacher in advisory. Is the total number of students proportional to the number of teachers? Teachers 1 Students 26

9. The City Pool costs 8 per day to visit during the summer. There is also a 25 yearly registration fee. Is the total cost proportional to the total number of days visited? Day 1 Cost 33

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!!!

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: x number of pizzas sold y Total Cost 11x 2 y

Sal’s Pizzeria sells large pizzas EXAMPLE 1 for 11 but charges a 2 delivery fee per order.

Proportional or Non-proportional? 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 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?