Question 468148
As we know two lines are perpendicular if and only if their slopes are negative 

reciprocals of one another {{{m[1]=-1/m[2]}}} or {{{m[1]*m[2]=-1}}}

Since the equation of one line is y=3x-4, its slope is {{{m[1]=3}}}

The slope of the perpendicular line will be {{{3*m[2]=-1}}}<=> {{{m[2]=-1/3}}}

Now we write the equation of the line that passes through (-1, 2), and has the 

slope {{{m[2]=-1/3}}}: y-2=-1/3(x+1), converting it in the standard form we get:

3y-6=-x-1 <=> x+3y=5 or in slope-intercept form {{{y=-(1/3)x+5/3}}}.