6.6Horizontal and Vertical Lines

A horizontal line has equation $y = k$ : the same $y$ for every point, so gradient $0$ . A vertical line has equation $x = h$ : the same $x$ for every point, so the gradient is undefined, and it cannot be written as $y = mx + c$ at all.

A horizontal line and a vertical line. Every point on

y = 3

has the same

y

; every point on

x = -2

has the same

x

Identifying special lines

State the gradient of the line $\displaystyle x = -2$ and the gradient of the line $\displaystyle y = 7$ . Which line passes through the point $\displaystyle (0, 7)$ ?

Show solution▾

x = -2

is a vertical line.

Its gradient is undefined.

y = 7

is a horizontal line.

Its gradient is

0

The point

(0, 7)

has

y

-coordinate

7

, so it lies on the line

y = 7

Now you try

The diagram shows two straight lines, Line 1 and Line 2. Write down the equation of Line 2.

Show solution▾

Line 2 is horizontal, so every point on it has the same

y

-coordinate.

It crosses the

y

-axis at

5

, so

y = 5

for every point on it.

y = 5

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