Inverse Variation

Q:  Suppose that y varies inversely with x.  When x= 10, y= 2. find y if x=5.

A:  OK.  The equation that we always go to for inverse variation is:  y = k/x (x and y are our variables, and k is our constant).  You always need to find k!  So, they gave us one set of data points: x = 10, y = 2.  Plug that in:

y = k/x

2 = k/10

Now, solve for k:

(10)*2 = k/10 * 10

20 = k

So, now we know the equation is: y = 20/x (since k = 20).  The question says: find y if x = 5…. So, plug in 5 for x:

y = 20/x

y = 20/5

y = 4

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