Variation and Power Modelling

Direct Variation

Two values are said to be directly proportional to each other when they follow the equation y=kx, where k is a proportionality constant.

When two values are directly proportional to each other, we use the ∝ to denote this relationship:
y ∝ x
 
You might have realized that this corresponds to the linear equation y = mx, crossing the origin. This means that for two values to be directly proportional to each other, the line must be linear (straight) and hence the gradient must be a constant.
 
Please note that directly proportional to is equivalent to varies directly. It always crosses the origin.
 
Inverse Variation
 
Two values are said to be inversely proportional when they follow the equation yx = k, where k is a proportionality constant. You can also interpret this as y = k/x. As y increases, x decreases. As y is multiplied, x is divided.
 
When plotted against a graph, it should look like:
Inverse Variation
 
Please note that inversely proportional to is equivalent to varies indirectly. The y ∝ 1/x can be used to denote this relationship. When two values are inversely proportional to each other, the y-axis and x-axis re the asymptotes of the graph. This means that the line should never cross the y-axis or the x-axis; it has no intercepts.
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