Question:
A line passes through $\left(x_{1}, y_{1}\right)$ and $(h, k)$. If slope of the line is $m$, show that $k-y_{1}=m\left(h-x_{1}\right)$.
Solution:
The slope of the line passing through $\left(x_{1}, y_{1}\right)$ and $(h, k)$ is $\frac{k-y_{1}}{h-x_{1}}$.
It is given that the slope of the line is m.
$\therefore \frac{k-y_{1}}{h-x_{1}}=m$
$\Rightarrow k-y_{1}=m\left(h-x_{1}\right)$
Hence, $k-y_{1}=m\left(h-x_{1}\right)$