# Thread: converting y to x

1. ## converting y to x

I have been working with finding area's and volumes lately and I always seem to get caught up when I need to convert y values into x values, is there some easy method to doing this.

For example

$\displaystyle y=2\sqrt{x-1} ..... x=\frac{y^2}{4}$

I just have a hard time seeing why this is.

If possible please show a general method.

2. Well there is no general method as such for rearranging formulas, but if you remember, whatever we do to one side an equation we must do to the other, then it becomes easy.

For example we can add and subtract, multiply and divide, take squares and roots of numbers from both sides:

$\displaystyle a+1=b \iff a=b-1 \text{ Subtract 1 from each side}$
$\displaystyle x-c=y \iff x=y+c \text{ Add c to each side}$
$\displaystyle y=\sqrt{x}\iff x=y^2 \text{ Square both sides}$

etc...

And this applies to any arithmetic operation.

3. y/2 = (x-1)^0.5

y^2/2^2 = x- 1

x = (y^2 / 4) + 1 ? OK?

Now solve my problem

http://www.mathhelpforum.com/math-he...nces-hard.html