6.4 Equation of Straight Lines (Part 2)


6.4.2 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:
yy1xx1=y2y1x2x1Let (x1,y1)=(2, 4) and (x2,y2) = (5, 6)y4x2=6452y4x2=233y12=2x43y=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
xa+yb=1x5+y(6)=1x5y6=1


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

(a)



(b)



(c)