Mathematics Question (quite easy)

[Brian Le]

I know this question is easy and stupid, but I really need to confirm this.

The formula for direct variation is y = k/x. You have the equation x = 5y. Tell whether x and y show direct variation, inverse variation, or neither.

To find out what variation the equation shows, y must be isolated. To do that, we divide each side by 5, giving us y = x/5. Thus, x and y show direct variation. Why is that? Is it because x is not in denominator?

 

[ShadenSmith]

As far as I've always understood it, if x is in the numerator it's direct, if it is in the denominator, it's indirect. That's because it is directly part of the multiplication of y when in the numerator, but not so if in the denominator.


If that's incorrect or unclear please correct me/elaborate.

 

[Lucas Garron]

The formula for direct variation is y = k/x.

Sure? As one goes up, the other goes down. That sounds like inverse to me.

You have the equation x = 5y. Tell whether x and y show direct variation, inverse variation, or neither.

Well, direct. Each varies directly and constantly depending on variation of the other.

To find out what variation the equation shows, y must be isolated. To do that, we divide each side by 5, giving us y = x/5. Thus, x and y show direct variation. Why is that? Is it because x is not in denominator?

Sorta. Consider it y=x*(1/5), which is really y=kx for k=1/5.

Isolting the y (especially in more difficult problems) allows you to see what y does compared to (i.e. as a function of varying) x.

Direct: y = kx , y goes up with x.
Inverse: y = k/x , y goes down as x goes up (and vice-versa).
Neither: y=0; y doesn't depend on x. Or, say y=sin(x). x doesn't go anywhere, really.


(Note: I'm assuming k>0)

 

[Brian Le]

Opps, sorry about stating that y = k/x was direct. It's inverse, ahaha.

Anyway, thanks Lucas!