A line with zero slope is a line that have the same value of y, the response variable, for any value of x, the independent variable.
For example:
x | y
-----------
0 | 2
1 | 2
10 | 2
50 | 2
If we calculate the slope, we will have:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]As y2=y1 for any point, the slope is 0.