Chapter 8.5, Problem 23E

To determine

To find:

The slope of a parallel line and the slope of a perpendicular line for the line with the given equation.

Answer to Problem 23E

The slope of perpendicular lineto our given line is $1$ .

The slope of parallel lineto our given line is $-1$ .

Explanation of Solution

Given:

An equation: $y=-x-9$ .

Concept used:

We know that the slope of a perpendicular line to a given line is negative reciprocal of the slope of the given line. The product of slopes of two perpendicular lines is -1.

We also know that the slopes of two parallel lines are equal.

Calculation:

Let mbe the slope of perpendicular line to our given line.

We can see from our given equation that it is in slope-intercept form and its slope is $-1$ .

We will find the slope of perpendicular line to our given line as shown below:

  $\begin{array}{l}-1\cdot m=-1\\ \frac{-1\cdot m}{-1}=\frac{-1}{-1}\left(\text{Dividing both sides by }-1\right)\\ m=1\end{array}$

So, the slope of perpendicular line to our given line is $1$ .

We can see that the slope of our given line is $-1$ . Since slope of two parallel lines is equal, therefore, the slope of parallel line to our given line would be $-1$ .