Lesson 5: 7-5 Variation Functions
Duration of Days: 3
Lesson Objective
1. Recognize and solve direct and join variation problems.
2. Recognize and solve inverse and combined variation problems.
1. How can a graph illustrate the relationship between two values?
2. What variable must stay the same to create a direct variation?
3. What is the first step in solving a proportion?
Direct Variation
Constant of Variation
Joint Variation
Inverse Variation
Combined Variation
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
SAT questions related to rational functions: 1-3-13, 6-3-12
The type of variation present can sometimes be identified from a table of values for x and y. If the quotient x/y has a constant value, y varies directly as x. If the product xy has a constant value, y varies inversely as x.
While building skateboard ramps, Yu determined that the best ramps were the ones in which the length of the top of the ramp was 1.5 times as long as the height of the ramp. The length of the top of the ramp depends on the height of the ramp. The length increases as the height increases, but the ratio remains the same, or is constant. The equation l/h=1.5 can be rewritten as l=1.5h. The length varies directly with the height of the ramp.
Discuss with students how to write variation equations that include a constant of variation.
Have students write the formulas using different colors for each variable and another color for k. Do this for each of the three types of variation: direct, joint, and inverse.
McGraw Hill resources
McGraw Hill resources