Chapter 1.5, Problem 6CFU

To determine

To find: whether graphs of given equations are parallel, coinciding, perpendicular, or none of these.

Answer to Problem 6CFU

Perpendicular

Explanation of Solution

Given information:

  $\begin{array}{l}y=-6x-2\mathrm{...}\text{(1)}\\ y=\frac{1}{6}x-8\mathrm{...}\text{(2)}\end{array}$

Calculation:

Compare equation (1) with slope intercept equation to get,

  $\begin{array}{l}m=-6\\ b=-2\end{array}$

Compare equation (2) with slope intercept equation to get,

  $\begin{array}{l}m=\frac{1}{6}\\ b=-8\end{array}$

Since, the slope of both the lines is opposite reciprocal of each other i.e. $\left(\perp m=-\frac{1}{m}\right)$ . So, the two lines are perpendicular to each other.