Two variables are proportional if they have a common ratio.
An example of proportional values is the price of gasoline. Signs advertising the price
of gas give it in dollars per gallon. The price posted
is the common ratio. To calculate the total price, multiply the price per gallon
times the number of gallons. Given a price of $3.00 per gallon, This can be
expressed as a function t(g)=3g, where
g is the number of gallon of gas and
t(g) is the total price of the gas. The graph in figure 1
represents this relationship.
Figure 1: Graph of the function t(g)=3g which is directly proportional.
Variables can be
or inversely proportional.
The example of gasoline prices is an example of directly proportional.
An example of inversely proportional is the time it takes to make a
trip as a function of speed. The faster you go, the quicker (less time) you get there.
This can be expressed with the function t(s)=100÷s
where t(s) is the time it takes to make the
trip, 100 is the distance, and
s is the speed of travel. Figure 2 contains a graph of this relationship.
Figure 2: Graph of t(s)=100/s which is inversely proportional.
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