Interactive graph of a straight line y = mx + c with controls for gradient and intercept, showing both intercepts, a rise over run triangle, and a second line that is parallel, perpendicular or intersecting, with the point of intersection marked and solved

Two rules, two lines, one shared point

Every non-vertical line is y = mx + c: m is the rate of change, c is the value at x = 0. Put a second line on the same axes and the pair can meet once, never, or everywhere. Raise the gradient, then the intercept, and watch where the green line cuts the axes and where it meets the amber one.