Aim: How do we find inverse variations and graph the hyperbolas?

Do Now:It takes 4 painters 6 days to paint a house. How long would it take the following number of painters to paint the same house?a) 8 b) 2 c) 1 d) x

HW: Worksheet

In the do now, time and rate vary inversely. That is, as one value increases the other will decrease.

If x and y vary inversely then xy = k, a non-zero constant.This constant is known as the constant of variation.

To solve a problem that involves inverse variation, we use the formula

2211 yxyx

Example:

If 10 people rent a limo each person needs to pay $5, how much will each person pay if 20 people share the rent equally?

$2.5

How do we graph a inverse variation function?

Example: Graph: xy = 6

First of all, we need to solve y in terms of x, then set up a table of values x

y6

x y

-6

-3

-2

-1

1

2

3

6

Math Composer 1. 1. 5http: / / www. mathcomposer. com

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

10

x

yMath Composer 1. 1. 5http: / / www. mathcomposer. com

Graph:

xy = 6

The graph approaching to x-axis vertically, but it never touches the x-axis.

The graph approaching to y-axis horizontally, but it never touches the y-axis.

Both x-axis and y-axis are called asymptotes

Asymptote an asymptote is a straight line that is a close approximation to a particular curve as the curve goes off to infinity in one direction. The curve becomes very, very close to the asymptote line, but never touches it.

The cost of hiring a bus for a trip to Niagara Falls is $400. The cost per person (x) varies inversely as the number of persons (y) who will go.a) Find the cost per person if 25 persons go on the trip.b) Find the number of persons who are going if the cost per person is $12.50.

1.) Draw the graph of xy = -122.) Is this graph a function? y

x

The direct variation is when one variable increases the other also increases or when one variable decreases the other also decreases.

The formula is

Example: one dozen of eggs costs $2.00, how much does 180 eggs cost?

6y = 180, y = 30