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.
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:
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.