# 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!