## 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.