Proportional vs. Non-proportional

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Proportional vs. Non-proportional

• Saturday, August 13, 2016

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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.
• We will make tables and look at the relationship
  between the variables to determine
  proportionality.

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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.

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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.

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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
x y
0 2
3 8
5 12
9 20
10 22
Proportional? ______
Proportional? Ratio Ordered Pair
Ratio _________ Equation____________
Ordered Pair _________
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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.
Proportional ? _________
Proportional ? _________
Line does not go thru the origin
Why?
Why?
Line goes thru the origin
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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.
Proportional? ______
Equation ___________
Ordered Pair _________
Ratio _________
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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 10x
y 3x 1
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• 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
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• 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
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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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Example 1 Identify Proportional Relationships

• Sals Pizzeria sells large pizzas for 11 but
  charges a 2 delivery fee per order.
• Write an equation to fit this situation

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Example 1
Sals Pizzeria sells large pizzas for 11 but
charges a 2 delivery fee per order.
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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 Jos towels to dry. How
long did it take Sues?
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HOMEWORK finish handout