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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.

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@Jay: the equations you wrote down are both equations for the line you've been given, which passes through (2, -3). You are supposed to be finding the equation of a different line which also passes through (2, -3). –  Qiaochu Yuan Aug 29 '10 at 21:30
    
If the course for which this is homework is a linear algebra course (a course about vectors and matrices) rather than a secondary-school algebra/advanced algebra/precalculus course or a college algebra course, then I have a different solution method to suggest than the one in my answer. –  Isaac Aug 29 '10 at 21:37
    
@Qiaochu, the original line isn't passing through (2, -3). –  Nick Dandoulakis Aug 29 '10 at 21:59
    
@Jay: Hint: write the general equation of the family of straight lines perpendicular to your given line and use the information that (2,-3) is a point which lies in the unique line perpendicular to it. –  Américo Tavares Aug 29 '10 at 22:38
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The lines perpendicular to the line $ax+by=c$ all have the form $bx-ay=d$. –  Robin Chapman Aug 30 '10 at 6:37

1 Answer 1

up vote 5 down vote accepted

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 $(2,-3)$.

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Thank you Isaac. This was the correct answer. –  Jay Aug 31 '10 at 11:15

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