SOLUTION: 1. Two points, as we know, determine a line segment. To compute the slope of the line, we can take the points in either order. Explain WHY this is so. Give an example to help

Algebra ->  Linear-equations -> SOLUTION: 1. Two points, as we know, determine a line segment. To compute the slope of the line, we can take the points in either order. Explain WHY this is so. Give an example to help       Log On


   

Question 14313: 1. Two points, as we know, determine a line segment. To compute the
slope of the line, we can take the points in either order. Explain WHY
this is so. Give an example to help explain.

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
If the points are taken as P with coordinates (p,q) and A with coordinates (a,b)
then the slope of the line PA is given by the formula
Difference in Y coordinates / Difference in X coordinates
= (b-q)/(a-p)...It does not matter for this purpose whether we take the coordinates of A first or those of P first as long as we take the same order for calculating the difference of both Y and X cordinates of the 2 points.It is
easy to see that
Slope of PA = (b-q)/(a-p) = (-(q-b))/(-(p-a))= (q-b)/(a-p)= Slope of AP
Viewing it from the physical sence , slope of a line is the Tangent of the angle the line makes with X axis in the positive (anticlockwise)direction. The line afterall makes the same angle with X axis , whether we look at it as PA or AP and hence its tangent which is the slope of the line is also same whichever way we take the line segment.