6.4 Equations of Straight Lines (Part 1)

6.4 Axes Intercepts and Gradient

(A) Formula for gradient:
1. Gradient of the line joining (x1, yl) and (x2, y2) is:


2. Gradient of the line with knowing x–intercept and y–intercept
    is:

3. The gradient of the straight line joining P and Q is equal to the 
    tangent of angle θ, where θ is the angle made by the straight line 
    PQ and the positive direction of the x-axis.


(B) Collinear points
The gradient of a straight line is always constant i.e.the gradient of AB is equal to the gradient of BC.




Example 1:
The gradient of the line passing through point (k, 1 – k) and point 
(–3k, –3) is 5.  Find the value of k.

Solution:
Gradient,  m = y 2 y 1 x 2 x 1 3 ( 1 k ) 3 k k = 5 3 1 + k 4 k = 5 4 + k = 20 k 21 k = 4 k = 4 21
Example 2:
Based on the diagram below, find the gradient of the line.
Solution:
Gradient,  m = ( y  intercept x  intercept ) = ( 5 10 ) = 1 2

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