solve a pair of linear equations in two variables.

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 the point C and is parallel to the line ‘l’. Observe how the positions of the lines change when we move the points A, B and C.
Questions to think about When we move the points A, B and C, find the relation between a_1/a,b_1/b and c_1/c . What do we get? What happens to a_1/a,b_1/b and c_1/c when the two lines overlap?