Chapter 4, Problem 5SAP

To determine

To find:.Slope of a line perpendicular to the line represented by the equation $3x-6y=12$ .

Answer to Problem 5SAP

A. $-2$

Explanation of Solution

Given information: One line is $3x-6y=12$

A. $-2$

B. $-\frac{1}{2}$

C. $\frac{1}{3}$

D. $\frac{1}{2}$

E. 2

Calculation:

Given line segment is $3x-6y=12$ .

Converting given line in the form of y = mx + b to get:

  $\begin{array}{l}3x-6y=12\\ -6y=12-3x\\ 6y=3x-12\\ y=\frac{3}{6}x-\frac{12}{6}\\ y=\frac{1}{2}x-2\end{array}$

Comparing it with y = mx + b , we get

  $m=\frac{1}{2}$

Since the other line is perpendicular so is slope would be $-\frac{1}{m}$ , which gives us:

  $-\frac{1}{\frac{1}{2}}=-2$

So the correct answer is A.