The standard way to do this is to find the gradient and substitute to find the y intercept and tidy up, or you could use y-y_1= m(x-x_1) etc.

I don't understand why it is not possible to substitute the points directly into ax+by+c =0. Two points should be sufficient to find the equation of the line but if you take this approach we have only 2 equations and 3 unknowns?

2a+5b+c = 0

3a+10y+c= 0

Why can't this be

*made*to work?

Tell me if i am talking nonsense!