Chapter 3.4, Problem 54E

To determine

To find: whether the lines are parallel, perpendicular, or neither.

Answer to Problem 54E

Neither

Explanation of Solution

Given information:

Let the slope of line $l_1$ and $l_2$ be $m_1$ and $m_2$ respectively. The slope values for both the lines are given below.

  $\begin{array}{l}{m}_1=\frac{1}{4}\\ m_2=4\end{array}$

Calculation:

The slope of two parallel lines is equal. Since $m_1\ne m_2$ , so the lines are not parallel.

If two lines are perpendicular, then slope of one line is negative reciprocal of the other line i.e.

  $\perp m=-\frac{1}{m_l}$

Put the values of slope and check whether the lines are perpendicular

  $\begin{array}{l}{m}_1=-\frac{1}{m_2}\\ \frac{1}{4}\ne -\frac{1}{4}\left[\text{Put the values of }{m}_1\text{ and }{m}_2\right]\end{array}$

Since $m_1\ne -\frac{1}{m_2}$ , so the lines are not perpendicular.

Thus, the lines are neither parallel nor perpendicular.