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:
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:
= 
, the equation for the line is
x =
.
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.
