1. Direct and Inverse Variation SOL A8 by Robert Lotze, Moody Middle School

2. Direct Variation  The longer you shower, the more water you use.  You can describe this Relationship using Direct Variation

4. The national average for time in a shower is 12.2 minutes. The average shower head uses 6 gallons of water per minute. This means the average shower uses 73.2 gallons of water. How much water is this in a year for you? (how often do you shower?)

5. Here is a table to help you. X (minutes36912 Y(gallons18367290 A relationship exists between the number of minutes In a shower, and the gallons of water used. The equations for this table is: y = 6x This is called a direct variation. This means that as x increases, y increases, Or, as x decreases, y decreases

6. Another example Emma’s wages vary directly as the number of hours she works. If her wages for 5 hours are $29.75, how much will she be paid for 30 hours? Frist, find Emma’s hourly pay. Let x = number of hours worked, and let y = Emma’s pay. The value of k is the amount of money Emma is paid per hour. This is called the constant of the direct variation.

9. Your turn

11. Inverse Variation The length of a violin string varies inversely as the frequency of its vibration. In other words, the shorter the string the higher the pitch. A violin string 10 inches long vibrates at a frequency of 512 cycles per second. Find the frequency of an 8 inch string. You can describe this relationship using Inverse Variation

12. Inverse Variation

14. Your turn If you have ever seen or been on a seesaw, you will know that the heavier person has to sit closer to the fulcrum (pivot point) of the see saw to balance. This is a type of lever. This is also an inverse variation. The fulcrum is placed in the middle of a 20- foot seesaw. Chloe, who weighs 120 lbs., is seated 9 feet from the fulcrum. How far from the fulcrum should Anthony sit if he weighs 135 lbs.?

16. Your Turn

17. In Summary