Direct vs. Indirect (Inverse) Proportion
THE DIFFERENCE
Variation, in general, will concern two variables, say height and weight of a person, and how when one of these changes, the other might be expected to change. We have direct variation if the two variables change in the same sense, i.e. if one increases, so does the other. We have indirect variation if one going up causes the other to go down. An example of this might be speed and time to do a particular journey, so the higher the speed the shorter the time.
Describe the interaction of variables in direct proportion.
Using the examples provided as a guide, develop your own example of two factors that are
directly proportional:G
Describe the interaction of variables in indirect / inverse proportion.
Using the examples provided as a guide, develop your own example of two factors that are
indirectly proportional:
SYMBOLS
Normally we let x be the independent variable and y the dependentvariable, so that a change in x produces a change in y. For example, if x is the number of motor cars on the road and y is the number of accidents, then we expect an increase in x to cause an increase in y.
State what x and y each represent.
GRAPHS
When two variables are graphed, the graphs are different depending on whether or not the variables are directly proportional or indirectly / inversely proportional.
Examine these two graphs closely. Identify which graph shows a direct relationship between two variables and which shows an indirect / inverse relationship between two variables.
EQUATIONS
The relationship between x and y can be show in an equation. The symbol k is used as a constant – let’s randomly give it a value of 100. Here are two equations: xy = k and x/y = k.
Determine which of the two equations presented represents direct proportion and which represents indirect / inverse proportion. Choose numbers for x and y that will equal k. The value of k is 100. Then adjust thenumbers for x and y a few times keeping k equal to 100 to demonstrate relationships.
BONUS: Explain why the graphs wouldn’t both be straight lines - just opposite of each other. Why does one curve? Support this mathematically.