What is the easiest way to find the line perpendicular to a given line?

Lines that are perpendicular have slopes that are negative
reciprocals of each other.  What this means is if the slope for the first line is a/b
the perpendicular line would have a slope of -b/a.

Let's
start with an example with numbers so that you can see the full
process.

Find the line perpendicular to y = 1/3x + 2, that
crosses at point (3,2)

It is easiest to start with a line
in slope-intercept form. For our example we will use y = 1/3x + 2 as the original line.
1/3 is the slope so we know that the line goes up 1 unit and right 3 units. The 2 is the
y-intercept, this tells us that this line crosses the y axis at
(0,2).

To find the perpendicular line, the first step is to
find the negative reciprical of the slope 1/3.  Invert the fraction to 3/1 and add a
negative sign.  The new slope is -3. One point is given as (3,2). If you substitute
these into the equation with the new slope you can solve for the slope intercept and
complete the new equation.

y = -3x +
b

2 = -3(3) + b

2 = -9
+b

11 = b

y = -3x + 11
(substitute the new slope and y-intercept into the equation) is perpendicular to y =
1/3x + 2.

I hope that this example helps you understand how
to solve perpendicular lines in the future.