1. C HAPTER 4 EQ: How do I determine a proportional relationship?

2. P ROPORTIONAL VS. N ON -P ROPORTIONAL 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.

3. V OCABULARY 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.

4. I S IT P ROPORTIONAL ? 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.

5. P ROPORTIONAL R ELATIONSHIPS 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.

6. 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. Proportional ? _________ Why? Line goes thru the origin Why? Line does not go thru the origin

7. U SING 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.

8. U SING A GRAPH TO FIND A UNIT RATE

9. P ROPORTIONAL OR N ON - 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.

10. EX 1. and 2.) Tell if the following tables represent a proportional relationships. xy 510 816 1020 1428 2142 Proportional? ______ Ratio _________

11. E QUATIONS : 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!!!

12. Write an equation that fits this situation: Hint: Use your constant ratio!! Ex. 2) A lemonade recipe calls for 1.5 cups of lemon juice and 6 cups of cold water. Lemon Juice Cups of Water 1.56 312 4.518 624

13. D RAW THE GRAPH OF THE TABLE BELOW Cups of Water Lemon Juice Cups of Water 1.56 312 4.518 624

14. E XAMPLE 2 A lemonade recipe calls for 1.5 cups of lemon juice and 6 cups of cold water.

15. E XAMPLE 1 I DENTIFY P ROPORTIONAL R ELATIONSHIPS Sal’s Pizzeria sells large pizzas for $11 but charges a $2 delivery fee per order. Write an equation to fit this situation:

16. E XAMPLE 1 Sal’s Pizzeria sells large pizzas for $11 but charges a $2 delivery fee per order.