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Direct, Inverse and Joint Variation

Direct, Inverse and Joint Variation. December 10 Yes, this is where I really want to be. Direct Variation. A direct variation is a linear function that can be written in the form y= kx . Where k ≠ 0. The two variable ( x & y ) vary directly or are proportional.

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Direct, Inverse and Joint Variation

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  1. Direct, Inverse and Joint Variation December 10 Yes, this is where I really want to be...

  2. Direct Variation A direct variation is a linear function that can be written in the form y=kx. Where k ≠ 0. The two variable ( x & y ) vary directly or are proportional. The value of k shows the constant of variation of the dependent variable. Graph:

  3. Direct Variation 1: If y varies directly as x and y = 18 when x = 15, find ywhenx = 20. Ex 2: If y varies directly as x, and y = 3 when x = 10, find y when x = 4.

  4. Inverse Variation Form: y = or xy = k, where k is the constant of variation. Graph:

  5. Inverse Variation 2. : If a varies inversely as b and b = 4 when a= 16, find b when a = 3. Ex 4: If y varies inversely as x, and y = 10 when x = 20, find x when y = 16.

  6. Direct and Inverse together... 3. If z varies directly as y and inversely as x, and z = 4 when y = 3 and x = 6, find x when z = 16 and y = 2. 5. Suppose a varies directly with b and inversely with the square of c. If a = 12, b = 36, and c= 0.6, find a when b= 97 and c = 0.2.

  7. Joint Variation Occurs when 1 quantity varies directly as the ________________________of 2 or more other quantities. Form ________________________, x ≠ 0, z ≠ 0 4)If a varies jointly with b and c and inversely with d, find a when b = 6, c = 7, and d = -4, if a= 3, b = 3, c = -2, and d = -4.

  8. Let’s Try the Rest... 6) The length of rectangles of fixed area varies inversely as the width. Suppose the length of a rectangle is 22 mm when the width is 12 mm. Find the width when the length is 33 mm. 7) The area of a rectangle varies jointly as its length and width. If the area of a rectangle is 72 cm2 when the length is 12 cm and width is 6 cm, find the length when the area is 62.5 cm2 and the width is 2.5 cm.

  9. One More... 8) A car’s stopping distance varies directly with the speed it travels, and inversely with the friction value of the road surface. If a car takes 60 feet to stop at 32 mph, on a road whose friction value is 4, what would be the stopping distance of a car traveling at 60 mph on a road with a friction value of 2?

  10. Review: Do you know. . . Equation for a direct variation? Equation for an inverse equation? Equation for a joint variation? or for understanding the lesson.

  11. What’s Next?? • HOMEWORK: Handout

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