Question 475863
I think the simplest way is to start with the four collinear points, in which we have one line.


The next case would be involving the other six points: choose two of these six points, 6C2 = 15 ways to do it.


The final case would be to choose one of the four collinear points, then one of the six remaining points, in which 24 lines are determined (we do not overcount lines because no three of the other points are collinear).


The number of lines is 1+15+24 = 40.