L3 Partial Variation
Completion requirements
Unit D: Graphing
Partial Variation
Dave and Krista are students that work for a landscaping company during the summer. Each student receives $16 per hour to mow lawns. Krista, however, receives an extra $10 per day since she brings her own lawnmower. Dave’s and Krista’s daily earnings are displayed in the graph below.
Direct variation was studied in Unit D: Lesson 2. Compare the graphs of Dave’s and Krista’s daily wages to determine if either demonstrates direct variation.
Direct variation was studied in Unit D: Lesson 2. Compare the graphs of Dave’s and Krista’s daily wages to determine if either demonstrates direct variation.
| Characteristics of Graphs
Demonstrating Direct Variation |
Dave's Earnings
|
Krista's Earnings
|
|---|---|---|
| The graph is a straight line.
|
Yes | Yes |
| The rate of change is constant.
|
Yes, the rate of change for Dave's wage is $16 per hour.
|
Yes, the rate of change for Krista's wage is $16 per hour.
|
| The graph includes the ordered pair (0, 0), the origin.
|
Yes, the first point on Dave's graph is (0, 0).
|
No, the first point on Krista's graph is not (0, 0); it is (1, 10).
|
Dave’s line graph demonstrates direct variation, but Krista’s does not. It does not demonstrate direct variation since the line does not pass through the point (0, 0). Krista’s wage represents a different kind of relationship. In this lesson, how to identify partial variation will be discussed.
By the end of this lesson, you will be able to
- identify and describe the characteristics of linear relations represented by graphs, tables of values, number patterns, or equations
- relate slope, or rate of change, to a linear relation
- sketch the graph for a given table of values
- create a table of values for a given equation of a linear relation
- create a graph to represent a set of data
- write an equation for a partial variation relationship