Question 131791
To put an equation of the form {{{ax+by=0}}} into slope-intercept form {{{y=mx+b}}}, you simply solve the equation for y.  That means do anything legal to get a single y on the left side of the equal sign and everything else on the right.  Your problem is larger than just that.  Because either there is an error in the answer key in the back of your book, or you are looking at the wrong answer.  {{{x-4y=8}}} is most assuredly not equivalent to {{{y=3x-2}}}


{{{x-4y=8}}}


Add -x to both sides:
{{{-4y=-x+8}}}


Divide both sides by -4 (the coefficient on y)
{{{y=x/4-2}}}


The green line is {{{y=3x-2}}}, and the red one is the correct {{{y=x/4-2}}} answer.
{{{graph(400,600,-5,5,-5,5,x/4-2,3x-2)}}}


If it is an error in the answer key, don't sweat it.  It certainly isn't the first time and highly unlikely to be the last.