$A$ line passes through $(x_{1}, y_{1})$ and $(h, k)$. If the slope of the line is $m$,show that $k - y_{1} = m(h - x_{1})$.

(N/A) The slope of a line passing through two points $(x_{1}, y_{1})$ and $(h, k)$ is given by the formula:
$m = \frac{k - y_{1}}{h - x_{1}}$
It is given that the slope of the line is $m$.
Therefore,we have:
$\frac{k - y_{1}}{h - x_{1}} = m$
Multiplying both sides by $(h - x_{1})$,we get:
$k - y_{1} = m(h - x_{1})$
Hence,the equation is proved.