**Theorem 1.5**: If
(*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2})
are points on the
line whose equation is *y* =
*mx* + *b* then the distance between them
is

**Proof**: By Theorem 1.1,
the slope between them is

so, clearing denominators gives us

If we substitute this into the distance formula,

we get

Factor out an (*x*_{2} - *x*_{1})^{2}

which equals