$y \,=\, mx$
It is an equation of a straight line when a straight line passes through origin with some slope in two dimensional Cartesian coordinate system.
A straight line is passing through origin $(O)$ of the Bi-dimensional Cartesian coordinate system and $P$ is any point on the straight line. The straight line is represented by $\overleftrightarrow{OP}$ in geometry.
The slope of the straight line is $m$ and it is equal to the tan of angle theta.
$m \,=\, \tan{\theta}$
Now, find the value of $\tan{\theta}$ in terms of coordinates of right triangle $QOP$.
$\tan{\theta} \,=\, \dfrac{PQ}{OQ}$
$\implies \tan{\theta} \,=\, \dfrac{y}{x}$
Geometrically, tan of angle theta is equal to slope of straight line $m$.
$\,\,\, \therefore \,\,\,\,\,\, m \,=\, \dfrac{y}{x}$
The equation of a straight line when a straight line passes through origin with some slope can be written in algebraic form from the mathematical relation of slope of line with coordinates of any point on that straight line.
$\,\,\, \therefore \,\,\,\,\,\, y \,=\, mx$
It is similar to the slope intercept form of a straight line. It can be derived from slope intercept form linear equation by placing zero as $x$ or $y$ intercept of the line.
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