Direct variation means that one variable is equal to a constant times another variable. That is, #y=kx#. Rearranging the equation above, we get #y=2x+5# which is obviously not in the form #y=kx#, but it can be proven a bit more convincingly that this is not direct variation by noting that whenever one variable varies directly as another, when one is zero so is the other. That is, if #y=kx# then when #x=0#, #y=0#. This is intuitively true because any #k# times #0# will be #0#. Plugging #x=0# and #y=0# into the equation above we get a contradiction, thus when #x=0#, #y!=0# so the equation is not direct variation.

#(0)-5=2(0)#

#"-"5=0#

#"false"#