A new Equation of a Straight Line

Question

A new straight line equation?

$\frac{(y-y_2)}{(y-y_1)}=\frac{(x-x_2)}{(x-x_1)}$ is also a straight line equation?

Answer 1

The graph will be straight when your slope is constant.

The slope is given by $\frac{y_1-y_2}{x_1-x_2}$ with $y_1$, $y_2$, $x_1$, $x_2$ being coordinates at two points.

In a straight line the slope is a constant.

So $\frac{y_1-y_2}{x_1-x_2}=\frac{y_3-y_4}{x_3-x_4}$

So let's consider $3$ points. The slope between these should be same as they make a straight line.

So, $\frac{y-y_1}{x-x_1}=\frac{y-y_2}{x-x_2}$.

So, $\frac{y-y_2}{y-y_1} =\frac{x-x_2}{x-x_1}$.

So, I suppose this is not a new equation.