The equation of a line through the origin:

$$ax + by = 0$$

A sample:

$${}$$

You can drag the red dot to change the slope of the line, that is, influence $a$ and $b$. The vector pointing to the red dot represents the direction vector.

Change the value of $x$ by dragging the slider:

The equation of a line through the origin:

$$ax + by = c$$

A sample:

$${}$$

You can drag the red dot to change the slope of the line, that is, influence $a$ and $b$. The vector pointing to the red dot represents the direction vector. The length of this vector influences $c$.

Change the value of $x$ by dragging the slider: