1. Chapter 8 Variation

2. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Relations between Changing Quantities In a fixed hour, we go further if we ride faster.

3. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation It takes less time to complete a 100 m race when we run faster. Relations between Changing Quantities

4. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Lighting up more bulbs can make the room brighter. Relations between Changing Quantities

5. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation We pay more if we travel a longer distance. Relations between Changing Quantities

6. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation With the same amount of money, we get less food if the price is higher. Relations between Changing Quantities

7. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation We experience certain relations among changing quantities in our daily life.  Speed   Distance   Speed   Time   Number of candles   Brightness   Distance   Fares   Price   Quantity bought  Relations between Changing Quantities

8. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Direct Variation (I)  x   y  and x   y  The meaning of y varies directly as x:  The value of keeps unchanged  Symbolically, y  x  In the form of equation, y  kx where k is a non-zero constant.

9. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation The graph of equation y  kx is a straight line passing through the origin. Direct Variation (I)

10. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Direct Variation (II)  x 2   y  and x 2   y  The meaning of y varies directly as x 2 :  The value of keeps unchanged  Symbolically, y  x 2  In the form of equation, y  kx 2 where k is a non-zero constant.

11. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Direct Variation (II) The graph of equation y  kx 2 is a curve.

12. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation where u  x 2 Direct Variation (II) The graph of equation y  ku is a straight line passing through the origin.

13. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Inverse Variation  x   y  and x   y   The value of xy keeps unchanged The meaning of y varies inversely as x:  Symbolically,  In the form of equation, or xy  k where k is a non-zero constant.

14. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Inverse Variation The graph of equation is a curve.

15. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Inverse Variation The graph of equation y  ku is a straight line passing through (but does not include) the origin. Graph of y against u u where

16. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Joint Variation  If h is fixed, then y varies directly as r 2.  If r is fixed, then y varies directly as h.  Symbolically, y  hr 2  In the form of equation, y  khr 2 where k is a non-zero constant. The meaning of y varies jointly as h and r 2 :

17. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Partial Variation  y is the sum of two parts.  One part of y varies directly as h.  Other part of y varies directly as b.  In the form of equation, y  k 1 h  k 2 b where k 1 and k 2 are non-zero constants. The meaning of y partly varies directly as h and partly varies directly as b:

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