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

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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