1. 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?

2. 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.

3. 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!

4. 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 = •10=k or k = 150
5•30=k or k =150 Note k stays constant.
y = 150/x is the equation!

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

6. 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

7. 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!

8. 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

9. 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 = 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

10. 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 = 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

11. 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 =

12. 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

13. 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….

14. the ORIGIN!!!!!

15. The graph of Indirect Variation