Direct Variation

The formula for direct variation is y = kx where k is a constant (k = y/x) value

For example if y varies directly with x, and y = 6 and x = 30 then we can find he value of k,

6 = k(30)
k = 1/5

So if we know y = 10 we could find x.
10 = 1/5x
x = 50

If we know x = 20
y = 1/5(20)
x = 4

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Inverse Variation

The formula is y = k/x (k = x * y) as x gets bigger y gets smaller because we are dividing the constant by x. As x goes up, y goes down. As x goes down, y goes up.

If we have 20 workers take 100 hours to build a house then our k value is 2000.

We have hours = 2000/workers.

If number of workers gets bigger, hours will go down. If number of workers goes down, houw will go up.

20 = 2000/100 - this is the ratio we nust keep.

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Say that y varies inversely with x, if y = 2 and z = 6, write the equation

2 = k/6 so k =12. So the equation is y = 12/x

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Say that the time it takes to build a house varies inversely with the numbers of workers. So, if if takes 80 hours with 12 workers, how long will it take with 20 workers

80 = k/12
k = 960

H = 960/20
H = 48

What if there were 30 workers? H = 960/30. H = 32

If building the house took 40 hours, how many workers were there?
40 = 960/x
40x = 960
x = 24


Joint Variation

The formula for Joint Variation is y = kyz

So if the area of a triangle varies jointly with the base b, and the height h. So if the Area is 20, and the base is 5 and the height is 8 then we get:
20 = k(5)(8) and we find the k is 1/2.

So if we are given that the area is 60 and the height is 3:
60 = 1/2(b)(3) b = 40