5.2 Gradient of a Straight Line in the Cartesian Coordinates (Sample Questions)


Example 1:
Given that a straight line passes through points (-3, -7) and (4, 14). What is the gradient of the straight line?

Solution:

Let (x1, y1) = (-3, -7) and (x2, y2) = (4, 14).
Gradient of the straight line 
= y 2 y 1 x 2 x 1 = 14 ( 7 ) 4 ( 3 ) = 21 7 = 3


Example 2:









The gradient of the straight line PQ in the diagram above is

Solution:
Let (x1, y1) = (12, 0) and (x2, y2) = (0, 7).
Gradient of the straight line PQ
= y 2 y 1 x 2 x 1 = 7 0 0 12 = 7 12



Example 3:
A straight line with gradient -3 passes through points (-4, 6) and (-1, p). Find the value of p.

Solution:
y 2 y 1 x 2 x 1 = 3 p 6 1 ( 4 ) = 3 p 6 3 = 3 p 6 = 9 p = 3

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