c hapter 4 eq: how do i determine a proportional relationship?
TRANSCRIPT
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CHAPTER 4
EQ: How do I determine a proportional relationship?
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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.
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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.
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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.
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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
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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
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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.
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USING A GRAPH TO FIND A UNIT RATE
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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
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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 _________
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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!!!
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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
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DRAW THE GRAPH OF THE TABLE BELOW
Cups of WaterLemon Juice
Cups of Water
1.5 6
3 12
4.5 18
6 24
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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