Chapter 5.6, Problem 23P

Open-Ended Write the equations of two lines whose graphs are perpendicular to one another.

To determine

To write: The equations of two lines whose graphs are perpendicular to one another.

Answer to Problem 23P

The equations of two lines whose graphs are perpendicular to one another are given below:

  $\begin{array}{l}y=2x+1\\ y=-\frac{1}{2}x+3\end{array}$

Note: Answer may vary.

Explanation of Solution

Given information:

Two lines whose graphs are perpendicular to one another.

If the graphs of the lines have to be perpendicular to one another, then the product of their slopes must be equal to $-1$ . Following are the equations of two lines whose graphs are perpendicular to one another.

  $\begin{array}{l}y=2x+1\\ y=-\frac{1}{2}x+3\end{array}$

Conclusion:

We can observe that the above written equations have the slopes whose product is equal to $-1$ , so their graphs are perpendicular to one another.