How Do You Determine Whether Two Variables Are Directly Proportional?
• The ratio is a constant, usually denoted by k Understand what the phrase directly proportional means. A very common misconception is that two variables are directly proportional if one increases as the other increases. Two variables are said to be directly proportional if, and only if, their ratio is a constant for all values of each variable. Thus when one variable is divided by the other, the answer is always a constant. • Directly proportional variables In the example on the right, y increases as x increases. Importantly, their ratio is the same for all values. They are directly proportional. • Variables that are not directly proportional In this example, y does increase as x increases. In fact, y increases uniformlywith x. However, the ratio of y to x is not the same for all values. This relationship is not that of direct proportion. Obtain a sufficient number of sets of values of both the variables. You may be able to obtain them from calculation, or through practical experiment
