Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Learning Goals: I can determine if a relationship is linear or non-linear I can determine if a relation represents a partial variation or a direct variation I can identify the initial value

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Take a look at this data: Age of Tree Height of Tree (years) (meters) 1 2 4 3 6 8 5 10 12 7 14 16 9 18 20 Is there a perfect linear relationship here? How do you know? We look at the difference table!

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation First Differences  

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Take a look at this data: Is there a linear relationship here? How do you know? We look at the difference table!

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation First Differences  

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Conclusion……… When there is a linear relationship between the data each row in the difference table will be the same. When there is a non-linear relationship between the data the differences are not the same for every row in the difference table.

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Be careful….. To calculate the first differences, the x-values must be increasing by the same amount and they must be in order! Look at these examples.

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation First Differences  

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation First Differences  

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation How can we tell by looking at the graph if the relationship is linear or nonlinear?

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation A barrel contained 42L of water. The water was leaking out. The table shows how the volume of water in the barrel changed every hour. Describe the relationship

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation How much water would be in the barrel after 6h? What assumptions did you make?

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Which gym would you choose? Cardio Crazy Gym charges $25 to sign-up and $5 a month. Pumping Iron Gym charges $8 a month, with no sign-up fee.

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Cardio Crazy - $25 and $5/month Pumping Iron - $8/month

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation So, now which gym would you choose? Choose Cardio Crazy if you are planning on being with the gym for more than 8 months. Choose Pumping Iron if you are planning on being with the gym for less than 8 months.

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation What looked different about the graphs for the two gyms?

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Direct Variation – when a graph of a linear relationship passes through the origin. The initial value is zero.   Partial Variation – when a graph of a linear relationship passes either above or below the origin, but not through initial value is not zero. Initial Value: Is the value of the dependent variable (y-value) when the independent variable (x-value) is zero.

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Cardio Crazy – Direct or Partial Variation? How can you tell by looking at the graph? How can you tell by looking at the equation? Pumping Iron– Direct or Partial Variation? How can you tell by looking at the graph? How can you tell by looking at the equation?

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Look at the following graphs. Decide if they represent direct or partial variation.

Lesson 8: Partial Variation and Direct Variation Unit 4: Linear Relations Lesson 8: Partial Variation and Direct Variation Practice p115 #2, 4 p145 #1, 2ab, 4, 5 Handout