Here we have two straight lines; first is ax+by+c=0 (red) and the second one is a_1 x+b_1 y+c_1=0 (green). Line ‘l’ (green) passes through two points A and B. Line ‘m’ (red) passes through two points C and D. Observe how the positions of the lines change when you move the points A, B, C and D. E is the point where line ‘l’ and ‘m’ intersect

Questions to think about
When the lines intersect each other then what is the relation between a_1/a,b_1/b and c_1/c ?