6.4 Equation of Straight Lines (Part 2)

6.4 Equation of Straight Lines

Case 1
1. The gradient and coordinates of a point are given.
2. The equation of a straight line with gradient m passes through the 
     point (x1, y1) is:

Example 1:
A straight line with gradient –3 passes through the point (–1, 5). Find the equation of this line.

Solution:
yy1 = m (xx1)
y – 5 = – 3 (x – (–1))
y – 5 = – 3x – 3
y = – 3x + 2

Case 2
1. The coordinates of two points are given.
2. The equation of a straight line joining the points (x1y1)
     and (x2, y2) is:
Example 2: 
Find the equation of the straight line joining the points (2, 4) and 
(5, 6).

Solution:
y y 1 x x 1 = y 2 y 1 x 2 x 1 Let ( x 1 , y 1 )=( 2, 4 ) and ( x 2 , y 2 ) = ( 5, 6 ) y4 x2 = 64 52 y4 x2 = 2 3 3y12=2x4 3y=2x+8

Case 3
1. The equation of a straight line with x–intercept “a” and
    y–intercept “b” is:
Example 3: 
Find the equation of the straight line joining the points (5, 0) and
(0, –6).

Solution:
x–intercept, a = 5, y–intercept, b = –6
Equation of the straight line
x a + y b =1 x 5 + y ( 6 ) =1 x 5 y 6 =1

The equation of a straight line can be expressed in three forms:

(a)


(b)


(c)