A horizontal line is one the goes lefttoright, parallel to the xaxis of the coordinate plane. All points on the line will have the same ycoordinate. In the figure above, drag either point and note that the line is horizontal when they both have the same ycoordinate.
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 ycoordinate, and the slope is zero.
The equation of a horizontal line is
y = b 
Where:

The two points A,B on the line are at (7,7) and (39,7). The second coordinate in each pair is the ycoordinate which are 7, and 7. Since they are equal, the line is horizontal.
Since the line passes the yaxis at 7, the equation of the line is
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.
For more see Teaching Notes