The formula for the slope of a line is given by:
m = (y2- y1)/(x2 - x1)
where (x1,y1) and (x2,y2) are two points in the line.
1) When a line has a slope with value 0, this means the line is horizontal. In this case all values of y are the same for any value of x.
Thus, an example of two point in a line with slope 0 can be:
(2,6) and (7,6)
These points are the save value of y, if you replace thes values into the formula for m the result is zero because you have zero in the denominator of the right side of the equation.
2) When a line has an undefined slope, this means that the line is vertical. In this case all values of x are the same for any value of y.
Thus, an example of two points in a line with undefinied slope can be:
(2,-4) and (2,6)
If you replace the previoues values into the formula for m, you get 0 in the denominator of the right side of the equation, that is, you have a division by zero, which means that there is an indetermination there.