SAT Math: Algebra

Variation Problems

If x and y are directly proportional and y = 10 when x = -5, what is the value of x when y = 6?  

A.  -9

B.  -5

C.  -3

D.  -1

E.  8


Knowsys Method

Read the question carefully.  What kind of relationship does x have with y?

Identify the bottom line.  You are looking for a value of x.

Assess your options.  Please do not try to draw a coordinate grid for this type of problem!  There is a very simple formula that you can use to determine direct variation.  It is y = kx.  The variable k represents a constant number.  All you need to do is plug in your first values for y and x to determine k, which controls the relationship between x and y.  Then use that value for k to find the next value for x.

Attack the problem.  Once you have a plan of attack, use it!  The first pair of numbers that you are given is y = 10 and x = -5.  Plug these numbers into your formula and solve for k.

y = kx

10 =  -5k

-2 = k

Now you have the number that controls the relationship between x and y.  Use that value for k to find x when y = 6. 

y = kx

6 = -2x

 -3 = x

Loop back.  You solved for your bottom line, so all you need to do is select your answer!


The correct answer is (C). 

This is a medium level question.


Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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