Question

When you graph the equations y = -2 and x = 5 on the same graph, would the line representing y = -2 be vertical, horizontal, or perpendicular to the line representing x = 5?

Answer 1

The line representing y = -2 is a horizontal line on the graph, while the line representing x = 5 is vertical. When graphed on the same axes, these two lines will intersect at a right angle and therefore are perpendicular to each other.

Step-by-step explanation:

When graphing the equation y = -2, since there is no x-variable involved, this represents a horizontal line at y = -2 on the graph. Conversely, for the equation x = 5, as it contains no y-variable, this represents a vertical line at x = 5 on the graph. When both lines are graphed on the same set of axes, they will be perpendicular to each other since one is horizontal and the other is vertical. This is in line with the concept that horizontal and vertical lines on a graph, which are defined by equations in the form of y = constant or x = constant respectively, are always perpendicular to each other.