# 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:

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
$\begin{array}{l}\frac{x}{a}+\frac{y}{b}=1\\ \frac{x}{5}+\frac{y}{\left(-6\right)}=1\\ \frac{x}{5}-\frac{y}{6}=1\end{array}$

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

(a)

(b)

(c)