Question 22849
If the given equation is y=3/2x -3, this means that the slope of the given line is {{{3/2}}}.  The slope of any line parallel to this line is also going to have a slope of {{{3/2}}}, but that's another question.  In this case, you need the slope of a line that is PERPENDICULAR to the given line.  This slope would be the NEGATIVE RECIPROCAL of the slope {{{3/2}}} which would be {{{-2/3}}}.


The equation of a line in slope intercept form is {{{y=mx+b}}}.  So the slope of a line perpendicular to the given line must have slope of {{{-2/3}}}, so the equation would be {{{y= (-2/3)x+b}}}, where b could be any value, since no other restrictions were given.  Usually the problem requires that the line pass through a given point, in which case you must also solve for b.  But this too is another question!


Final answer, {{{y= (-2/3)x+b}}}, where b represents any number (which would also turn out to be the y intercept).


R^2 at SCC