Thread: Find the equation of a parallel line

Find the equation of a line which is parallel to the line mx + ny + c = 0 and passing through the point (2,3).


The given answer is: m(x-2)+n(y-3) = 0, but how do I get there?

The slope of the line is

The equation of the line is

Originally Posted by fcabanski

Find the equation of a line which is parallel to the line mx + ny + c = 0 and passing through the point (2,3).


The given answer is: m(x-2)+n(y-3) = 0, but how do I get there?

The lines for fixed and form a series of parallels as varies.

So the line you seek is found by finding the value of so that goes through . That is:



or:



CB

Why are the x and y values subtracted from x and y in red dog's answer?

Originally Posted by fcabanski

Why are the x and y values subtracted from x and y in red dog's answer?

The equation of a line passing through the point and having the slope is

Originally Posted by fcabanski

Find the equation of a line which is parallel to the line mx + ny + c = 0 and passing through the point (2,3).

Any line parallel to has the same form .
If it contains the point this must be true:
or

Thanks everyone!