Which of the following equations has (have) graphes consisting of two perpendicular lines?
I. xy=0
II. |y|=|x|
III. |xy|=1

Options

A. only I
B. only II
C. only III
D. only I and II

Answer

D

Explanation

Graph I consists of the lines x=0 and y=0, which are the coodinate axes and are therefore perpendicular. Graph II consists of y=|x| and y=|x|, which are at `+-45^(@)` to the coordinate axes and are therefore perpendicular. Graph III consists of the hypebolas xy=1 and xy=-1. Therefore, the correct answer choice is choice D.
There are two reasons why a graphing caculator solution is not recommended here. One is that equations, not functions, are given, and solving these equations so that they can be graphed involves two branches each. The other reason is that even with graphs, you would have to make judgments about perpendicularity. At a minimum, this would require you to graph the equations in a square window. [11]