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 slope-intercept form or point-slope 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.
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.
First solve the equation 2x + 3y = 1 for y to find its slope:
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 point-slope form to write the equation:
So 3x - 2y = -4 is the standard form of the equation of the line through (2, 5) that is perpendicular to 2x + 3y = 1.