Chapter 11.6, Problem 21PPE

To determine

To solve the function of inverse variation by graph $20=xy$

Answer to Problem 21PPE

Graph shown below.

Explanation of Solution

Given:

Given equation

  $20=xy$

Concept Used:

• In inverse variation $xy=k$ or $x\propto \frac{1}{y}$
• if $k>0$, graph will be plotted on first and third quadrant
• if $k<0$, graph will be plotted on second and fourth quadrant

Calculation:

In order to solve the equation $20=xy$

Or we can say $x=\frac{20}{y}$

Now on the basis of eqn. we have to draw a table

And putting the values in $x$ and $y$

X	x = 20 / y	(x, y)
-20	x = 20 / y y= - 1	(-20, -1)
-15	x = 20 / y y= -1.33	(-15, -1.33)
-10	x = 20 / y y= - 2	(-10, -2)
-5	x = 20 / y y= -4	(-5, -4)
0	x = 20 / y y= 0	Undefined
5	x = 20 / y y= 4	(5, 4)
10	x = 20 / y y= 2	(10, 2)
15	x = 20 / y y= 1.33	(15, 1.33
20	x = 20 / y y= 1	(20, 1)

Now in the above table $x=\frac{20}{y}$

Here the constant of variation $k$ , is $20$ , as given $k>0$ the graph will be plotted on 1^st and 3^rd quadrant. and it is inverse variation.

  

Thus, the solution is correct.