Directly varying quantities given graphs, tables, or statements are identified and problems involving direct variation are solved.
After completing this tutorial, you will be able to complete the following:
Direct variation is a type of proportionality relation between two varying quantities. Two quantities are proportional if they are constant multiples of each other. More specifically, two variables x and y vary directly if there is a nonzero constant k such that Y = K . X . The constant k is called the constant of variation.
Examples of direct variation:
Directly varying quantities are commonly represented by statements, graphs, or tables. The form of each representation is given below. For example, given that x and y vary directly, the following statement provides enough information to find the constant of proportionality:
y is 20 when x is 10.
Graphs can also be used to represent direct variation, in which case the graph must be a straight line and pass through the origin. If the graph is a straight line, but does not pass through the origin, then the relationship it represents cannot be a direct variation.
Direct variation should not be confused with linearity. Two quantities are linearly related if they have a constant ratio of change. This constant ratio is called the rate of change, or slope:
This is different from the condition imposed by direct variation in that the quantities themselves have a constant ratio.
Finally, note that direct variation is sometimes called direct proportionality, in which case the constant of variation is called the constant of proportionality.
|Approximate Time||30 Minutes|
|Pre-requisite Concepts||Students should know the concepts of ratio, and rate; be able to solve proportions and linear equations; and be able to graph linear equations.|
|Type of Tutorial||Concept Development|
|Key Vocabulary||application of direct variation, constant of proportionality, constant of variation|