What is it and how do I know when I see it? Indirect Variation What is it and how do I know when I see it?

Another way of writing this is k = xy Definition: Y varies indirectly as x means that y = where k is the constant of variation. Another way of writing this is k = xy In other words: * As X increases in value, Y decreases or * As X decreases in value, Y increases.

X Y 4 12 6 8 Examples of Indirect Variation: Note: X increases, 4, 6, 8 And Y decreases. 12, 8, 6 X Y 4 12 6 8 What is the constant of variation of the table above? Since y = we can say Therefore: 4•12=k or k = 48 6•8=k or k = 48 6•8=k or k =48 Note k stays constant. y = 48/x is the equation!

X Y 30 5 15 10 Examples of Indirect Variation: Note: X decreases, 30, 15, 5 And Y increases. 5, 10, 15 X Y 30 5 15 10 What is the constant of variation of the table above? Since y = we can say Therefore: 30•5=k or k = 150 15•10=k or k = 150 5•30=k or k =150 Note k stays constant. y = 150/x is the equation!

What is the constant of variation for the following indirect variation? -9 9 -1/9 1/9 X Y 1 9 3 18 .5

Is this an indirect variation Is this an indirect variation? If yes, give the constant of variation (k) and the equation. X Y 24 2 12 4 Yes! k = 24•2 or 48 Equation? y = 48/x

Is this an indirect variation Is this an indirect variation? If yes, give the constant of variation (k) and the equation. X Y 7 5 15 2 20 2.5 No! The y-values decrease, but then increase! The k values are also different!

Which is the equation that describes the following table of values? y = -2/x y = 2/x y = -200/x y = 200/x X Y 50 4 20 10 Answer Now 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Using Indirect Variation to find unknowns (y = k/x) Given that y varies indirectly with x, and y = 12 when x=4, Find y when x = 12. HOW??? X Y 4 12 ? 2 step process 1. Find the constant variation k = xy or k = 12•4 = 48 k=48 2. Use y = k/x. Find the unknown (y). y=48/12 y= 4 Therefore: Y =4 when X=12

Using Indirect Variation to find unknowns (y = k/x) Given that y varies indirectly with x, and y = 100 when x=25, Find x when y = 500. HOW??? 2 step process X Y 25 100 500 1. Find the constant variation. k = yx or k = 100•25 K = 2500 2. Use y = k/x. Find the unknown (x). 500 = 2500/x x = 5 Therefore: X = 5 when Y = 500

Using Indirect Variation to solve word problems A gas with volume 45 cubic inches is under a pressure that is 75 pounds per square inch. Find the pressure when the volume is 80 cubic inches. Step One: Find points in table. X (volume) Y (pressure) 45 75 80 ? Step Two: Find the constant variation and equation: k = xy or k = 45•75 = 3375 y = 3375/x Step Three: Use the equation to find the unknown. y = 3375/80 y = 42.1875

Using Indirect Variation to solve word problems A gas with volume 30 cubic inches is under a pressure that is 40 pounds per square inch. Find the pressure when the volume is 60 cubic inches. Step One: Find points in table. X (volume) Y (pressure) 30 40 60 ? Step Two: Find the constant variation. k = xy or k = 30•40 = 1200 k = 1200 Step Three: Use the equation to find the unknown. y=k/x y = 1200/60 y = 20

Indirect Variation and its graph With indirect variation the equation is y = k/x Note: Because one variable is always doing the opposite of the other variable, the graph will never go through….

the ORIGIN!!!!!

The graph of Indirect Variation