× = × , which tells that vt is a constant. Here, vt = . In such a case, we say the variables v and t are inversely proportional. Observe that the graph of equation like vt = will not be a straight line.
Inverse variation implies that as one variable increases, the other variable decreases. Visualising Indirect variation: Look at the adjacent graph. It is a graph of the equation xy = . We have taken only the [positive values of x , y.
The table of values is: Fig. . Scale x axis cm = mins y axis cm = km = Algebra This is an illustration of inverse variation or indirect variation. The graph is a part of a curve called Rectangular Hyperbola.
Example . A company initially started with workers to complete the work by days. Later, it decided to fasten up the work increasing the number of workers as shown below. Number of workers ( x ) Number of days ( y ) (i) Graph the above data and identify the type of variation.
(ii) From the graph, find the number of days required to complete the work if the company decides to opt for workers? (iii) If the work has to be completed by days, how many workers are required? (i) Fig. .
From the given table, we observe that as x increases, y decreases. Thus, the variation is an inverse variation. Let = k ⇒ > xy k k is called the constant of variation. From the table, ´ ´ ...
k ´ Therefore, = xy Plot the points ( , ), ( , ), ( , ) of ( , ) and join to get a free hand smooth curve (Rectangular Hyperbola). Scale x axis cm = workers y axis cm = days xy =