Direct & Indirect Variation - Greenebox Tutoring



Direct & Indirect Variation

These problems look complicated because they look like word problems, but it's really only two formulas.  Direct variation is the formula y = kx and Indirect is y = k/x

 

So basically if something varies directly (or jointly) it will be multiplied by the k, if it varies indirectly or inversely, k will be divided by it.

 

If the sentence says to find the constant of variation (or proportionality), that's the "k", just fill in the y and x values and solve it.

 

The only thing that changes is that sometimes the y and x will be called something else.

 

Example:  The Volume of the oil in the barrel varies directly as the Temperature. If V = 27 when T=3, then find the constant of variation (or constant of proportionality).

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Since Volume comes first in the sentence, it's the "y", and the word "directly" is in there

so the formula is y = kx, but we need to use the  letters that they use, so it's V = kT.  

Now fill in the values (Note: the k is always a k, it never changes)

V = kT

27 =k(3)

or

27 = 3k

9 = k

So the constant of proportionality k = 9

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Sometimes the problems will continue.  They may say something like:

Now find the Volume if the Temperature is increased to 6 degrees.

 

You will use the same formula for the whole problem V = kT, but now T = 6, so we have 

  V = k(6)  which can't be solved because you can not solve an equation with more than one unknown

(we don't know V or k).

But we actually do know “k”, we found it in the first part of the problem, k = 9 .  So fill it in and find V.

V = (9)(6)

V = 56

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Sometimes there are more values than just the “x”, place them either next to or beneath the “k” depending on whether the sentence says they are directly or indirectly proportional to y. There may also be mathematical operations included with the variables.

Example: Write the equation for the problem: Y varies directly as twice x, and inversely as w squared.

y = [pic]

It may stop here, or it may give you x, y and w and ask you for k.

It may stop after finding k, or it may continue on and give you two values (you fill in the “k” you found before) and ask you for the fourth value.

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