**Theorem 1.9**: Given a
line whose equation is

and a point whose coordinates are

the equation of the unique line through the point, perpendicular to the line, is

**Proof**: By Theorem 1.8, there
will be a unique line
through the point
perpendicular to
the line whose equation is
* y* = *mx* + *b*. * * Since this line
is to be
perpendicular to
the line whose equation is
* * *y* = *mx* + *b*, * * its slope will
be the negative reciprocal of * * *m* * * or * * -1/*m*. * * If we substitute * * -1/*m* * * for
the slope in the formula
for the * * *y* * * intercept in Theorem 1.3,
we get

If we substitute this into the * * *y* = *mx* + *b* * * form of the equation for
the perpendicular
line, we get the desired
result.