Question 126983
Write, in function form:
{{{ 3x+4y=0}}}

First, you need to identify which of the two variables is the "{{{independent}}}" variable. Usually, x is the independent variable, so we'll first write the equation in terms of {{{x}}}, which means that we'll need to solve for {{{y}}}.

{{{ 3x+4y=0}}}………. add {{{-3x}}} to both sides
{{{3x –3x+4y =0 -3x}}} 
{{{ 4y =-3x }}} ………..Divide both sides by {{{4}}}
{{{4y/4 =-3x/4 }}} 
{{{y =-(3/4)x }}} 

Now, to write this in {{{function form}}}, we replace the {{{y}}} with {{{f(x)}}}, which is read as {{{f}}} of {{{x}}} or function of {{{x}}}. When an equation is written in {{{function}}} form, it is easy to identify the {{{independent}}} variable.  
That's the variable inside the parentheses of the {{{f(x)}}} or {{{x}}}.

{{{f(x) = -(3/4)x }}}