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:
![m=(y_2-y_1)/(x_2-x_1)](https://img.qammunity.org/2023/formulas/mathematics/high-school/78uaqhwt0aws3qfwxigaftpihnmb1gzxtp.png)
As y2=y1 for any point, the slope is 0.