Why is #\frac{4}{x}=y# not a direct variation equation?

Question

Avery Alexander · Accepted Answer

When you have a direct variation between two variables, this means that as one variable goes smaller, the other variable also goes smaller. When one variable goes larger, the other variable also goes larger. Now, let's examine what happens in the equation #4/x = y# #x = 1# #=> 4/1 = y#
#=> 4 = y# #x= 2# #=> 4/2 = y#
#=> 2 = y# #x = 10# #=> 4/10 = y#
#=> 0.4 = y# Notice as we increase #x# from #1# to #10#, #y# got smaller.
Looking from another perpective, as we decrease #x# from #10# to #1#, #y# got larger. This means that your equation is an inverse variation

Savannah Anderson · Answer

undefined The equation $ \frac{4}{x} = y $ is not a direct variation equation because it does not follow the form $ y = kx $, where $ k $ is a constant. In a direct variation equation, $ y $ is directly proportional to $ x $, meaning that as $ x $ increases or decreases, $ y $ changes proportionally. In the given equation, $ y $ is inversely proportional to $ x $, as $ y $ increases when $ x $ decreases and vice versa. Therefore, it does not represent a direct variation.