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

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.

Gradient, m= y 2 y 1 x 2 x 1 3( 1k ) 3kk =5 31+k 4k =5 4+k=20k 21k=4 k= 4 21
Example 2:
Based on the diagram below, find the gradient of the line.
Gradient, m=( y intercept x intercept )=( 5 10 )= 1 2