Inverse Variation
Do you remember? Direct Variation Use y = kx. Means “y varies directly with x. ” k is called the constant of variation In a situation like this, when one quantity goes up, the other goes up. When one quantity goes down, the other goes down also.
Example of direct variation • Tom makes $10 an hour. His wages vary directly to his hours • Rope is sold by the foot. The cost of buying rope varies directly to the amount you buy.
Inverse Variation when one quantity goes up, the other goes down proportionately. When one quantity goes down, the other goes up by the some proportion.
Inverse Variation This relationship is described as “y varies inversely with x. ” And can be represtented by k is the constant of variation
Example of inverse variation • The time an ice block takes to melt varies inversely with the room temperature. • In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board.
Ex 1. Y varies inversely as x, and y = 4 when x = 7. Find x when y = 14 1. Write an equation that relates x & y. k=28 2. Find y when x= -4. y= -7 Solve the problem in two parts. 1. Use the inverse variation equation to find k when they give you both x and y 2. Use k you found and the x they gave you to find x
Ex 2. Y varies inversely as x, and y = -6 when x = 8. Find y when x = 3 1. Write an equation that relates x & y. k= -48 2. Find y when x= 3. y= -16 Solve the problem in two parts. 1. Use the inverse variation equation to find k when they give you both x and y 2. Use k you found and the x they gave you to find x
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