**Theorem 1.7**: If we are
given a line and a
point not on the
line, then there is a unique
line, going through a given
point,
parallel to the given
line.

**Proof**: If we are given a
line, then that
line has a
slope, even if it is
infinite by
Theorems 1.1 and
1.2. Any
line
parallel to the given
line has the same
slope as the given
line by definition. If we are
given a point not on the
line and we are given the
line, then we are given a
point and a
slope, so by
Theorem 1.3, there is a unique
line through the
point having the same
slope as the given
line. Since it has the same
slope as the given
line, it will be
parallel to it by
definition.