What is the slope of a line that passes through points (a/3 , b/3) and (a , b)?

Slope is rise over run. Run is horizontal distance, left to right. Run is always positive because we always go left to right. Rise is the vertical change in that same distance. A negative rise means it drops. This example runs 2a/3 units from a/3 to a and rises 2b/3 units from b/3 to b so the slope is (2b/3)/(2a/3) which reduces to b/a.