10.1 Gradient of a Straight Line


10.1.1 Gradient of a Straight Line

The gradient of a straight line is the ratio of the vertical distance to the horizontal distance between any two given points on the straight line.

Gradient, m = Vertical distance Horizontal distance
Example:












Find the gradient of the straight line above.

Solution:
Gradient, m = Vertical distance Horizontal distance = 4 units 6 units = 2 3

10.1.2 Finding the Gradient of a Straight Line

The gradient, m, of a straight line which passes through P (x1, y1) and Q (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 P and 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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