1­9: Direct Variation Direct Variation​
: What is ​
Direct Variation​
? What is a ​
Constant of Variation​
? What is a ​
Constant of Proportionality​
? y
x = k or y = kx, where k ≠ 0. In ​
direct variation equations, the constant rate of change, or slope, is assigned the special variable k. A linear relationship is a direct variation ​
when the ratio of y to x is a constant k. We say y varies directly with x. When two variable quantities have a constant ratio, their relationship is called a ​
direct variation​
. The constant ratio is called the constant of variation​
. The ​
constant of variation ​
is also known as the constant of proportionality​
. Summary: Example 1a: Page 82 Example 2b: Page 83 Two minutes after a diver enters the water, he has descended 52 feet. After 5 minutes, he has descended 130 feet. At what rate is the scuba driver descending? The distance y traveled in miles by the Chang family in x hours is represented by the equation y = 55x. Identify the constant rate of proportionality. Then explain what it represents. 1. Setup all the ratios. 2. Simplify the ratios. 3. Write the answer with the labels. 1. Remember the equation: y = kx, where k represents the constant of proportionality. Summary: Note: Example 3c: Page 83 Not all situations with a constant rate of change are proportional relationships. Likewise, not all linear functions are direct variations. Two pounds of cheese cost $8.40. Show the cost of 1, 2, 3 and 4 pounds of cheese. Is there a direct variation? Explain. For direct ​
variation​
, it must be a straight line and go through the origin. Summary: