Chapter 11.7, Problem 5AYU

True or False The lines $2x+y=4$ and $4x+2y=0$ are parallel. (pp. 37-38)

To determine

True or False.

Answer to Problem 5AYU

Solution:

True, the lines are parallel.

Explanation of Solution

Given:

$2x + y = 4$

$4x + 2y = 0$

Theorem Used:

Two non–vertical lines are parallel iff their slopes are equal and they have different $y\text{-intercept}$.

Calculation:

$L1: 2x + y = 4$

$L2: 4x + 2y = 0$

$\begin{array}{ll}L1 \Rightarrow \hfill & y = - 2x + 4\hfill \\ L2 \Rightarrow \hfill & y = - 2x\hfill \end{array}$

This is of the form $y = mx + b$, where $m$ is the slope.
Therefore, the two lines has $\text{slope} = - 2$ and $L1$

has $y\text{-intercept} = 4$, $L2$ has $y\text{-intercept} = 0$.

So by the above theorem, these two lines are parallel.