Final answer:
A line with the equation y = 12 has a slope of 0, meaning any line parallel to it also has a slope of 0, while a line perpendicular to it has an undefined slope, indicating that it's a vertical line.
Step-by-step explanation:
For the graph y = 12, which is a horizontal line, the slope of a line parallel to it will also be 0 because parallel lines have the same slope. The slope of a line perpendicular to it will be undefined, which means that a perpendicular line is a vertical line with an equation in the form of x = a, where a is a constant.
In the context of slope and the Algebra of Straight Lines, the equation y = mx + b describes a line with slope m and y-intercept b. For y = 12, m = 0 and b = 12. A slope of 0 indicates no rise over the run, which is characteristic of a horizontal line. Hence, any line perpendicular to it has to be vertical, signifying an infinite slope or undefined slope.