5.2 Gradient of a Straight Line in Cartesian Coordinates

5.2 Finding the Gradient of a Straight Line

The gradient, m, of a straight line which passes through (x1, y1) and (x2, y2) is given by, 
 
mPQ  =  y 2 y 1 x 2 x 1
Example 1:

Find the gradient of the straight line joining two points Pand Q in the above diagram.
Solution:
P = (x1, y1) = (4, 3), Q = (x2, y2) = (10, 5)

Gradient of the straight line PQ
= y 2 y 1 x 2 x 1 = 5 3 10 4 = 2 6 = 1 3


Example 2:
Calculate the gradient of a straight line which passes through point A (7, -3) and point B (-3, 6).

Solution:
A = (x1, y1) = (7, -3), B = (x2, y2) = (-3, 6)
Gradient of the straight line AB
= y 2 y 1 x 2 x 1 = 6 ( 3 ) 3 7 = 9 10

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