Lesson 7.9 Identifying Proportional Relationships

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Presentation transcript:

Lesson 7.9 Identifying Proportional Relationships Essential Question: How do you identify a proportional relationship?

Before we start… ITunes is having a major sale on music right now. Songs cost $0.50 each! What is your cost if you buy… 4 songs? 8 songs? 12 songs? 20 songs? Do you notice a pattern?

What is a proportion? An equation that states that two ratios are equivalent

What does it mean to be proportional? Two quantities always have the same size in relation to each other. They have the same ratio. One variable is always the product of the other variable and a constant.

A rope’s length and weight can be proportional A rope’s length and weight can be proportional. 40 meters of rope weighs 2 kilograms 200 meters of rope weighs 10 kilograms

What is the constant of proportionality? The value that relates the two amounts Ex. You are paid $20 an hour, 20 is the constant of proportionality

What does a proportional relationship look like? You can represent these with tables, graphs or equations. Equations have the form 𝑦=𝑘𝑥, where k is the constant of proportionality

How do you identify proportional relationships? Test pairs of values in a table to see if they are equivalent ratios. Graph pairs of values to see if they form a straight line that passes through the origin. Test pairs of values to see if they are related by the equation, 𝑦=𝑘𝑥.

Are these quantities proportional? Hours Worked (x) 1 2 3 4 5 6 Total Earnings in $ (y) 12 24 36 48 60 72

Are these quantities proportional? x 1 2 3 4 5 y 7 14 21 28 35

Are these quantities proportional? x 1 2 3 4 5 y 6 12 18 40 200

Are these quantities proportional? x 1 2 3 4 5 y 8 16 24 32 40

Are the plotted points a proportional relationship?

Are the plotted points a proportional relationship?

Are the plotted points a proportional relationship?

Does the equation represent a proportional relationship? 𝑦=𝑥−8

Does the equation represent a proportional relationship? 𝑦= 4 5 𝑥

Does the equation represent a proportional relationship? 𝑦=3𝑥+7

Does the equation represent a proportional relationship? 𝑦=−6𝑥

How do you identify a proportional relationship?

Ticket Out the Door Is this a proportional relationship? Why? 𝑦=−3𝑥+2