Guided Notes on Direct and Inverse Variation



Guided Notes on Direct and Inverse Variation

I. Direct Variation: y varies directly as x or y is directly proportional to x

(y = kx) where k is the constant of proportionality or constant of variation

As x gets larger, y gets larger or as x gets smaller, y gets smaller.

A line with a y-intercept of 0 is a direct variation.

Data that represents direct variation:

|x | y |

|-1 | 3 |

| 0 | 0 |

|-2 | 6 |

| 4 |-12 |

What is the constant of proportionality? ___________

Example 1: If y varies directly as x and s=10 when y=9, then what is y when x=4?

Method: (You could use proportions.)

[pic] cross multiply and divide

10y = 36

y = 3.6

Example 2: When a bicycle is pedaled in a certain gear, it travels 16 meters for every 3 pedal revolutions. How many revolutions would be needed to travel 600 meters?

Method : [pic]

16x = 1800

x = 112.5

Problem 1: A refund r you get varies directly as the number of cans you recycle. If you get a $3.75 refund for 75 cans, how much should you receive for 500 cans?

II. Inverse Variation: y varies inversely as x or y is inversely proportional to x

( y = [pic] or xy = k ) where k is the constant of proportionality or constant of variation

As x gets larger, y gets smaller or as x gets smaller, y gets larger.

Data that represents inverse variation:

|x |y |

|3 |4 |

|2 |6 |

| 9 |[pic] |

|10 |[pic] |

|1 |12 |

What is the constant of variation? _________

To find multiply x

Example1: If y varies inversely as x and x=3 when y=9, then what is x when y=27?

[pic]

3(9)=x27

27=x27

27 27

x = 1

Example 2: If y varies inversely as the square of x and y = 20 when x =4, find y when x =5.

y = [pic]

y = 12.8

Problem 1: Find x when y = 3, if y varies inversely as x and x = 4 when y = 16.

Problem 2: The amount of resistance in an electrical circuit required to produce a given amount of power varies inversely with the square of the current. If a current of .8amps requires a resistance of 50 ohms, what resistance will be required by a current of .5 amps?

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