Chapter 8.5, Problem 24E

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 24E

The slope of perpendicular lineto our given line is $\frac{1}{7}$ .

The slope of parallel lineto our given line is $-7$ .

Explanation of Solution

Given:

An equation: $y=-7x+4$ .

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 $-7$ .

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

  $\begin{array}{l}-7\cdot m=-1\\ \frac{-7\cdot m}{-7}=\frac{-1}{-7}\left(\text{Dividing both sides by }-7\right)\\ m=\frac{1}{7}\end{array}$

So, the slope of perpendicular line to our given line is $\frac{1}{7}$ .

We can see that the slope of our given line is $-7$ . Since slope of two parallel lines is equal, therefore, the slope of parallel line to our given line would be $-7$ .