Try this
Drag the points A or B and note the line is horizontal when they both have the same
y-coordinate.

A horizontal line is one the goes left-to-right,
parallel to the x-axis of the coordinate plane. All
points on the line will have the same y-coordinate.
In the figure above, drag either point and note that the line is horizontal when they both have the same y-coordinate.

A horizontal line has a
slope
of zero. As you move to the right along the line, it does not rise or fall at all.
As you drag the points above, you can see that when the line is horizontal,
the points both have the same y-coordinate, and the slope is zero.

The equation of a horizontal line is

y = b

Where:

x

is the coordinate of any point on the line

b

is where the line crosses the y-axis (y intercept).

Notice that the equation is independent of x. Any point on the horizontal line satisfies the equation.

Examples

Fig 1. Is the line horizontal?

Determine if the line shown in Fig 1 is horizontal and write its equation.

The two points A,B on the line are at (7,7) and (39,7).
The second coordinate in each pair is the y-coordinate which are 7, and 7.
Since they are equal, the line is horizontal.

Since the line passes the y-axis at 7, the equation of the line is

y = 7

which can be read as "for all values of x, y is 7".

Things to try

In the figure at the top of the page, drag the points around and note how points on horizontal lines can have any x-coordinate,
but the y-coordinates are the same.

Click "hide details" Adjust the points to create a new horizontal line. Write down the equation of the line
and then click "show details" to verify your answer.

Limitations

In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place.
This can cause calculatioons to be slightly off.