Chapter 8.5, Problem 4C

To determine

To find:

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

Answer to Problem 4C

The slope of perpendicular lineto our given line is $\frac{1}{3}$ .

The slope of parallel lineto our given line is $-3$ .

Explanation of Solution

Given:

An equation: $y=-3x$ .

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 m be 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 $-3$ .

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

  $\begin{array}{l}-3\cdot m=-1\\ \frac{-3\cdot m}{-3}=\frac{-1}{-3}\text{ (Dividing both sides by }-3\text{)}\\ m=\frac{1}{3}\end{array}$

So, the slope of perpendicular line to our given line is $\frac{1}{3}$ .

We can see that the slope of our given line is $-3$ . Since slope of two parallel lines is equal, therefore, the slope of parallel line to our given line would be $-3$ .