Principles of Mathematics - MPM1DC

Unit 3: Linear Relations

Activity 8: Direct Variation

Content

Direct variation describes a situation where the dependent variable varies directly with independent variable. In mathematical terms, write y x. The algebraic model of a direct variation is in the form y = mx, where m is the rate of change.

For example: the Hamilton airport charges $39.95 a week for parking. Parking cost number of weeks parked. If you let C represent the cost of parking, and n represent the number of weeks, the algebraic model is C = 39.95n.

The graphical model is shown below.

This graph was created using Geometer’s Sketchpad. Check out the next content page for information on creating a graph using Geometer’s Sketchpad.

The graphical model of a direct variation situation will always pass through the origin (0, 0).

From this graph, determine:

1. The cost of parking in the lot for 5 weeks.
   Approximately $200.
2. How long can you park in the lot for $300?
   7.5 weeks

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