TITLE: Algebra - Find the equation of the line perpendicular to 3x+2y-4=0 going through point (2,-3)
QUESTION [5 upvotes]: I was wondering if you could help...
I have Math homework, I was hoping if you could check my answer.
Find the equation of the line perpendicular to $3x+2y-4=0$ going through point $(2,-3)$.
$y=\large\frac{-3x+4}{2}$  
$y = 2$
$x=-\large\frac{2(y-2)}{3}$  
$x=-3$
Therefore my equation is correct?
thanks for you help in advance guys.

REPLY [5 votes]: If two lines are perpendicular, the product of their slopes is -1.  This is often restated as the slope of the line perpendicular to a given line is the opposite reciprocal of the slope of the given line.  For example, the line $6x-15y+3=0$ has slope $\frac{2}{5}$, so a line perpendicular to it will have slope $-\frac{5}{2}$.
With that fact, you should be able to determine the slope of the line for which you are finding an equation, and you know a point on the line.  Those two pieces of information should be enough for you to write an equation of the line perpendicular to $3x+2y-4=0$ going through point $(2,-3)$.