Proportionality: How does "y = kx" become "x = (1/k)y" ?

So there's two small math facts you need to recall that make this work. One: Dividing by something is the same as multiplying by its reciprocal. And two: When you have an equation and you perform some operation on one side, you must always perform that same operation on the other side. Keeping these two facts in mind, what happens if you start with y = kx and divide by k?
 
Couple of other facts:

- in the given equation "kx" means "k (multiplied by) x" and

- k us not equal to zero
 
ksdhart2 said:
So there's two small math facts you need to recall that make this work. One: Dividing by something is the same as multiplying by its reciprocal. And two: When you have an equation and you perform some operation on one side, you must always perform that same operation on the other side. Keeping these two facts in mind, what happens if you start with y = kx and divide by k?
Click to expand...

I get y/k = x
 
And

y/k = x ↔ x=(1/k)y


I can understand that y/k can equal y(1/k), but why change the sides of x and y on the other sides of the equal sign, from y(1/k) = x to x = (1/k)y?


 
KWF said:
why change the sides of x and y on the other sides of the equal sign, from y(1/k) = x to x = (1/k)y?
Click to expand...
When we solve an equation for one symbol, the result acts like a formula for that symbol. We generally write formulas with the isolated symbol on the left-hand side of the equation.

For example, we generally write:

y = m*x + b

instead of:

m*x + b = y

However, both equations make the same statement; therefore, we can't say that one of them is "wrong". They're simply different forms of the same statement.

Any equation may be read from left-to-right or from right-to-left, without changing the meaning. (Mathematicians have a fancy name for this: The Symmetric Property of Equality.)

So, if you prefer to write y(1/k)=x, there's nothing mathematically wrong with that.

If you prefer to write (1/k)y=x, there's nothing wrong with that, either. :cool:
 
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