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 = 70 012 = 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 p6 1( 4 ) =3 p6 3 =3 p6=9 p=3