(i) Slope-intercept form:
is the equation of a straight line whose slope is and which makes an intercept on the -axis.
Find the equation of a line with slope and cutting off an intercept units one negative direction of – axis.
(ii) Slope-Point form:
Let a line have slope and let it pass through a point then the equation of the line is given by
Slope and then equation of line is
(iii) Two-Point form:
A line pass through two given points and . Then the equation of the line is given by
where slope of the line
Equation of the line is
(iv) Intercept form:
Let line have – intercept and – intercept . Then the equation is
Equation of the line where is
(v) Determinant form:
Equation of a line passing through and is
Let and be two points , then equation of the line is
(vi) Perpendicular /Normal Form:
is the equation of the straight line where the length of the perpendicular form the origin on the line is and this perpendicular makes an angle with positive -axis.
Equation of the line is
The normal form of equation is where
(vii) General form:
is the equation of a straight line in the general form. In this case, slope of line – intercept , – intercept
Find slope , – intercept and -intercept of the line
(viii) Parametric Form:
or is the equation of the line in parametric form, where is the parameter whose absolute value is the distance of any point on the line from the fixed point
The above form is derived from slope-point form of the line
Consider the equations of lines and given by
Slopes and of and are given by and respectively.
Case of Parallel Lines:
The lines and are parallel if or or
Therefore, we can write equation of as
If a line is represented by , the the equation of a line , parallel to , is given by .
If , in the equation of , either or is zero , then also the equation of , parallel to , is given by .
Since in this case, both and represent lines parallel to the same coordinate axes.
Case of Perpendicular Lines:
The lines represented by and being respectively vertical and horizontal are mutually perpendicular.
Now consider a line
We can write the equation of a line perpendicular to , as
The slopes of and , respectively and . The product of the slopes being , the lines are mutually perpendicular .
To write the equation of , perpendicular to , just interchange the coefficients of and in the equation of and write one of the coefficients by reversin its sign.