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### Inverse Variation

- An
*inverse variation*is a relation between two variables x and y in which their product is always equal to some nonzero constant k, called the*constant of variation*. We say that y*varies inversely*as x. - The graph of an inverse variation consists of two separate curves or
*branches*. The graph is undefined for either x = 0 or y = 0. The graph gets very large in absolute value as x gets close to 0. As x gets very large in absolute value, the graph gets close to the x-axis. - In many problems, information is given about values of x and y that satisfy a particular inverse variation. Use these values to find the constant k. Then use k to find a missing value corresponding to another given value.

### Inverse Variation

Assume that y varies inversely with x. If x

_{1}= 15 when y_{1}= 10 find x_{2}when y_{2}= − 6- x
_{1}y_{1}= x_{2}y_{2} - ( 15 )( 10 ) = x
_{2}( − 6 ) - [150/( − 6)] = x
_{2}

x

_{2}= − 25Assume that y varies inversely with x. If x

_{1}= 7 when y_{1}= 13, find y_{2}when x_{2}= 11- x
_{1}y_{1}= x_{2}y_{2} - ( 7 )( 13 ) = 11y
_{2}

[91/11] = y

_{2}Assume that y varies inversely with x. If x

_{1}= 14 when y_{1}= 7 find x_{2}when y_{2}= − [1/4]- ( 14 )( 7 ) = x
_{2}( − [1/4] )

x

_{2}= − 392Assume that y varies inversely with x. If x

_{1}= 8 when y_{1}= 4 find y_{2}when x_{2}= − [4/6]- ( 8 )( 4 ) = x
_{2}( − [4/6] ) - ( − [6/4] )( 8 )( 4 ) = x
_{2}

x

_{2}= − 48Graph the inverse variation xy = 12. Assume x to be only positive

- Identify equivalent form to xy = ky = [12/x]
- Make a table of points
x line 1 2 3 4 5 y line 12 6 4 3 [12/5]

Graph utilizing points

Graph the inverse variation 2xy = 40. Assume x to be only positive

- Identify equivalent form to xy = ky = [20/x]
- Make a table of points
x line 1 2 3 4 5 y line 20 10 [20/3] 5 4

Graph utilizing points

Graph the inverse variation x( − [y/3]) = − 13. Assume x to be only positive

- Identify equivalent form to xy = ky = [39/x]
- Make a table of points
x line 1 4 7 10 13 y line 39 [39/4] [39/7] [39/10] 3

Graph utilizing points

Identify the quadrants of the branches in the function xy = − 24

- Identify equivalent form to xy = ky = [( − 24)/x]
- Make a table of points
x line − 12 − 8 − 4 4 8 12 y line 2 3 6 − 6 − 3 − 2 - Graph utilizing points

Quardrants II and IV

Identify the quadrants of the branches in the function xy = [1/3]

- Identify equivalent form to xy = ky = [1/3x]
- Make a table of points
x line − 3 − 2 − 1 1 2 3 y line − [1/9] − [1/6] − [1/3] [1/3] [1/6] [1/9] - Graph utilizing points

Quadrant I and III

Graph the inverse variation 8x([y/4]) = 56

- Identify equivalent form to xy = ky = [28/x]
- Make a table of points
x line − 24 − 16 − 8 8 16 24 y line − [7/6] − [7/4] − [7/2] [7/2] [7/4] [7/6]

Graph utilizing points

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Inverse Variation

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro 0:00
- Direct Variation
- Inverse Variation 0:24
- Constant of Variation k
- Y Varies Inversely as X
- Graphing Inverse Variation 3:09
- Real World Applications
- Example
- Product Rule 10:19
- Alternate Form
- Finding Missing 4th Point
- Example 1: Graph Inverse Variation 11:36
- Example 2: Graph Inverse Variation 14:47
- Example 3: Find Missing Point 19:39
- Example 4: Find Missing Point 21:53

1 answer

Last reply by: Dr Carleen Eaton

Sat May 21, 2016 3:31 PM

Post by Kenosha Fox on May 17, 2016

For example 4: Find Missing Point, do I only divide when finding X2 and multiply when finding Y2?