Chapter 8.5, Problem 26E

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 26E

The slope of perpendicular lineto our given line is $\frac{6}{11}$ .

The slope of parallel lineto our given line is $-\frac{11}{6}$ .

Explanation of Solution

Given:

An equation: $11x+6y=18$ .

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.

Let us convert our given equation in slope-intercept form as shown below:

  $\begin{array}{l}11x+6y=18\left(\text{Given equation}\right)\\ 11x-11x+6y=18-11x\left(\text{Subtracting }11x\text{from both sides}\right)\\ 6y=-11x+18\\ \frac{6y}{6}=\frac{-11x}{6}+\frac{18}{6}\left(\text{Dividing both sides by }6\right)\\ y=-\frac{11}{6}x+3\end{array}$

We can see from our given equation that it is in slope-intercept form and its slope is $-\frac{11}{6}$ .

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

  $\begin{array}{l}-\frac{11}{6}\cdot m=-1\\ \left(-\frac{6}{11}\right)\cdot -\frac{11}{6}\cdot m=-1\cdot \left(-\frac{6}{11}\right)\left(\text{Multiplying both sides by }-\frac{6}{11}\right)\\ m=\frac{6}{11}\end{array}$

So, the slope of perpendicular line to our given line is $\frac{6}{11}$ .

We can see that the slope of our given line is $-\frac{11}{6}$ . Since slope of two parallel lines is equal, therefore, the slope of parallel line to our given line would be $-\frac{11}{6}$ .