Question 976194
we have:
Direct Variation 
When two variables, {{{x}}} and {{{y}}} vary {{{directly}}}, then  
{{{y = kx}}} where {{{k}}} is a constant called the "constant of proportionality." 
When there is {{{direct}}} variation between variables {{{x}}} and {{{y}}}, {{{doubling}}} the value of {{{x}}} will {{{always}}} result in {{{y}}} being {{{doubled}}}.  Also, if {{{x}}} is cut in half, then {{{y}}} is cut in half. 

Inverse variation 
When two variables, {{{x}}} and {{{y}}} vary {{{inversely}}}, then  
{{{y = k(1/x) }}}
or
{{{y = k/x}}}
or
{{{xy = k}}} 
where {{{k}}} is a constant called the "constant of proportionality." When there is {{{inverse}}} variation between variables {{{x}}} and {{{y}}}, {{{doubling}}} the value of {{{x}}} will {{{always}}} result in {{{y}}} being 
{{{cut}}} in {{{half}}}.  Also, if {{{x}}} is cut in half, then {{{y}}} is doubled. 


in your example, if {{{x=4}}} and {{{y=12}}} then {{{y=kx}}}=>{{{12=k*4}}}=>{{{k=12/4}}}=>{{{k=3}}} =>if {{{x=4}}} and {{{y=12}}} then the constant of proportionality is {{{3}}} 

so, yes, it would be {{{y=3x}}}