Chapter 8.5, Problem 5C

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 5C

The slope of perpendicular lineto our given line is $-\frac{1}{4}$ .

The slope of parallel lineto our given line is $4$ .

Explanation of Solution

Given:

An equation: $y=4x+10$ .

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 $4$ .

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

  $\begin{array}{l}4\cdot m=-1\\ \frac{4\cdot m}{4}=\frac{-1}{4}\text{ (Dividing both sides by }4\text{)}\\ m=-\frac{1}{4}\end{array}$

So, the slope of perpendicular line to our given line is $-\frac{1}{4}$ .

We can see that the slope of our given line is $4$ . Since slope of two parallel lines is equal, therefore, the slope of parallel line to our given line would be $4$ .