Question 223382
I'm not sure if the equation is {{{(2/3)y+4 = 2x}}} or {{{2/(3y) + 4 = 2x}}}. I'll do both and you pick the right one.<br>
When writing "y as a function of x" it means solve the equaiton for y and this is what I shall do:<ul><li>{{{(2/3)y+4 = 2x}}}<ol><li>Subtract 4 from each side:
{{{(2/3)y = 2x - 4}}}</li><li>Multiply both sides by the reciprocal of 2/3 (which is 3/2):
{{{(3/2)(2/3)y = (3/2)(2x-4)}}}
{{{y = 3x - 6}}}
This equation expresses y as a function of x.</li></ol><li>{{{2/(3y) + 4 = 2x}}}<ol><li>Multiply both sides by 3y:
{{{(3y)(2/(3y) + 4) = (3y)(2x)}}}. 
{{{2 + 12y = 6xy}}}</li><li>Subtract 12y from each side (to get the y terms together):
{{{2 = 6xy - 12y}}}</li><li>Factor out y on the right side:
{{{2 = y(6x - 2)}}}</li><li>Divide both sides by (6x-2):
{{{2/(6x-2) = (y(6x-2))/(6x-2)}}}
The (6x-2)'s cancel on the right:
{{{2/(6x-2) = y}}}
This equation expresses y as a function of x.</li></ol></li></ul>
(Note: a solution provided by another expresses x as a function of y which is not what the problem asks for.)