Horizontal lines have a slope of
0
. Thus, in the slope-intercept equation
*y* = *mx* + *b*
,
*m* = 0
. The equation becomes
*y* = *b*
, where
*b*
is the
*y*
-coordinate of the
*y*
-intercept.

*Example 1*: Write an equation for the following line:

Graph of a Line

*Example 2*: Write an equation for the horizontal line that passes through
(6, 2)
.

Since the line is horizontal,
*y*
is constant--that is,
*y*
always takes the same value. Since
*y*
takes a value of
2
at the point
(6, 2)
,
*y*
always takes the value
2
. Thus, the equation is
*y* = 2
.

Similarly, in the graph of a vertical line,
*x*
only takes one value. Thus, the equation for a vertical line is
*x* = *a*
, where
*a*
is the value that
*x*
takes.

*Example 3*: Write an equation for the following line:

Graph of a Line

*Example 4*: Write an equation for the vertical line that passes through
(6, 2)
.

Since the line is vertical,
*x*
is constant--that is,
*x*
always takes the same value. Since
*x*
takes a value of
6
at the point
(6, 2)
,
*x*
always takes the value
6
. Thus, the equation is
*x* = 6
.

Incidentally, the lines
*y* = 2
and
*x* = 6
are perpendicular to each other. In fact, all horizontal lines
*y* = *b*
are perpendicular to all vertical lines
*x* = *a*
. The usual relationship between the slopes of perpendicular lines does not work here, as we might expect, because the slope of a horizontal line is
0
which has no reciprocal.