I can find the equation of a line using the slope-intercept form if I have two points on the line.

However I was trying to do the same with the standard form of the equation of a line, $ax+by=c$, and I can't make it happen.

The way it looks, there are three unknowns and only two equations in our system, where we would have $$ax\_1+by\_1=c$$$$ax\_2+by\_2=c$$ I'm not sure what $c$ is in this context or how to get a value for it with just two points as total information.

If it turns out it's actually not possible to find the equation of a line using the standard form, why is that the case?