Page 146 - DMTH201_Basic Mathematics-1

Unit 5: Equations of Straight Lines

Notes

Notes We know, that the equation y = mx + c, contains two constants, namely, m and c. For
finding these two constants, we need two conditions satisfied by the equation of line. In all
the examples above, we are given two conditions to determine the equation of the line.

5.4 General Equation of a Line

As unit, you have studied general equation of first degree in two variables, Ax + By + C = 0,
where A, B and C are real constants such that A and B are not zero simultaneously. Graph of the
equation Ax + By + C = 0 is always a straight line.
Therefore, any equation of the form Ax + By + C = 0, where A and B are not zero simultaneously
is called general linear equation or general equation of a line.
Different Forms of Ax + By + C = 0

The general equation of a line can be reduced into various forms of the equation of a line, by the
following procedures:

Slope-intercept Form

If B 0, then Ax + By + C = 0 can be written as

A C
y = x or y mx c ... (1)
B B
A C
where m = and c .
B B
We know that Equation (1) is the slope-intercept form of the equation of a line whose slope is
A C
y
, and -intercept is .
B B
C C
If B = 0, then x , which is a vertical line whose slope is undefined and x-intercept is .
A A

Intercept Form

If C 0, then Ax + By + C = 0 can be written as:

x y x y
= 1 or 1 …(2)
C C a b
A B

C C
where a = and b .
A B
C
We know that equation (2) is intercept form of the equation of a line whose x-intercept is
A
C
and y-intercept is .
B

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