Question 89393: Write the inverse variation equation of the following. Y varies inversely with x and y = 9 when x = 14.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! The "varies inversely with x" means that as x gets bigger, y gets smaller and as x gets smaller,
y gets bigger.
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This relationship can be written as:
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where k is an unknown constant. Notice that as x gets bigger, the denominator of the fraction
on the right gets bigger, so the term on the right gets smaller. Think in terms of x being
10. Then make x bigger, say x = 100. k divided by 10 is bigger than k divided by 100, so
as x gets bigger, the term k divided by x (which equals y) is getting smaller.
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For this problem you are told that when y is 9, x is 14. So in the equation that contains
k you can substitute 9 for y and 14 for x. When you do that the equation becomes:
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You can eliminate the denominator on the right side by multiplying both sides by 14 to get:
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Multiply out the left side and the equation becomes:
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Now you can go back to the original equation and substitute 126 for k to get the answer you
are looking for. That answer is that the equation is:
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You can check this by letting x = 14 and you will get:
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So when x = 14, obviously y = 9. After that you can let x be any value (other than zero
because division by zero is not allowed) and you can calculate the corresponding value
for y. Again, you can let x be two values such as 1 and 100 and you will see that as
x gets bigger, the value of y will vary inversely because it gets smaller.
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Hope this helps you to understand the problem better.
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