What is the relationship between the linear equattions(in standard form) of two perpendicular lines?

Linear equation in standard form: ax+by=c. When I am given the equation of one line in standard form I have to go through this long process to find out what the perpendicular line's equation is. The problem always gives the point on a graph were the two lines intersect to help me find the answer. I realized that when I looked at the original problem which was ax+by=c, the perpendicular line would always come out to be bx-ay=n. I'm trying to find out the relation to "c" in the original equation to "n" in the equation of the line that is perpendicular. For example: Would ax+by=c be perpendicular to bx-ay=2c-8? The answer is no to that example.

What is the relationship between the linear equattions(in standard form) of two perpendicular lines?
I don't see why you say the answer is no in that example, because the answer is yes.





bx - ay = n is perpendicular to ax + by = c for *every* c. All you have to do is substitute in the point that you know to work out that constant.





For example, if you want to know the line perpendicular to 3x + 5y = 23 which goes through (1,4), the answer will be 5x - 3y = n for some n. n = 5*1 - 3*4 = -7. So the answer will be 5x - 3y = -7.

avender