TUTORIALS:

Standard Form of a Line
The graph of the equation x = 4 is a vertical line.
Because slope is undefined for vertical lines, the equation of this line cannot be
written in slopeintercept form or pointslope form. Only nonvertical lines can be
written in those forms. However, a vertical line can be written in standard form. For
example,
x = 4
can be written as
1 Â· x + 0
Â· y = 4.
Every line has an equation in standard form.
Example
Finding the equation of a line
Write an equation in standard form with integral coefficients for the line l through
(2, 5) that is perpendicular to the line 2x + 3y = 1.
Solution
First solve the equation 2x + 3y = 1 for y to find its slope:
2x + 3y 
= 1 

3y 
= 2x + 1 

y 

The slope is

The slope of line l is the opposite of the reciprocal of
. So line l has slope
and
goes through (2, 5). Now use the pointslope form to write the equation:
y  5 

Pointslope form 
y  5 

Distributive property 
y 



= 2 

3x  2y 
= 4 
Multiply each side by 2. 
So 3x  2y = 4 is the standard form of the equation of the line through (2, 5) that
is perpendicular to 2x + 3y = 1.
