The point slope formula is:
1) (y - y1) = m(x - x1)
where m represents the value of the slope, and (x,y) and (x1,y1) represent two points on a graph. Rearranging the equation gives:
2) m = (y - y1) / (x - x1)
If you have a slope of zero,
3) 0 = (y - y1) / (x - x1)
it means the numerator (y - y1) must also reduce to 0, which means the value of y and y1 must be the same. Zero divided by anything is always zero:
4) 0 = 0 / (x - x1)
A zero slope means the line has a value of y, is parallel to the x axis, and never intersects with it.
If the slope is undefined, it implies division by zero, which means x and x1 are the same value:
1) m = (y - y1) / (x - x1)
2) m = (y - y1) / 0
What that means is that the line has no slope; it's a vertical line running parallel to the y axis at value x.
For slope 1/2:
1) 1/2 = (y - y1) / (x - x1)
Which means that if the value of y changes by 1 unit, the value of x changes by 2 units, or if the rise (y value) changes by 1, the run (x value) changes by 2.