Sketch a few members of the straight lines through the origin. By eliminating parameters, derive a differential equation which describes this family.

Attempt

$\displaystyle y = mx$ (since there are infinite gradients)

$\displaystyle \frac{dy}{dx} = m$

but the correct answer was: $\displaystyle \frac{dy}{dx} = \frac{y}{x}$. I am not sure why.