Kathy's+Notes+-+Partial+and+Direct+variation

Direct variation – A relationship between 2 variables in which one varies directly as the other. In other words: when one variable is a constant multiple of the other. (Ex: y=kx)

Ex: If a car travels at a steady speed of 50km/h, the distance varies directly as the time. When the distance is doubled, the time is doubled. When the distance is tripled, the time is tripled. The distance is a constant multiple of time. If the distance is 0, the time is 0 and so it will always pass (0, 0).

In general, if y varies directly as x, the graph is a straight line passing through the origin (0, 0). This graph is a direct variation.



Partial variation = a relationship between 2 variables in which one varies partially as the other. In other words: one variable is a constant multiple of the other, plus a constant. (Ex: y=kx+c)

Ex: The total cost of renting a car is $20 and $1.00/km driven. When the cost is doubled, the km driven is doubled, plus the fixed cost, $20. When the cost is tripled, the km driven is tripled plus the fixed cost, $20. The km driven is a constant multiple of the cost plus the fixed cost (constant). Even if the km is 0, there would still be a fixed cost and so the graph would not start at (0, 0).

In general, if y varies partially as x, the graph is a straight line, but does not pass through the origin, (0, 0). This graph is a partial variation.



Therefore, we can categorize a linear relation as a direct or partial variation if it passes through the origin. If it does, it is a direct variation. If it doesn’t, it is a partial variation.