Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

True or False:

The lines $2x+y=4$ and $4x+2y=0$are parallel.

Step-by-Step Solution

Answer

The given statement is true.

Step 1. Given information.

Consider the given lines,

$$\begin{gathered} 2x+y=4, \\ 4x+2y=0 \\ 2x+y=0 \end{gathered}$$

Rewrite the equations in terms of y,

$$\begin{gathered} y=-2x+4 ...... \left(i\right) \\ y=-2x ...... \left(ii\right) \end{gathered}$$

Step 2. Reason for being true.

Consider the slope intercept form, $y=mx+c$.

Compare equations (i) with the slope intercept form,

$m_1=-2$

Compare equations (ii) with the slope intercept form,

$m_2=-2$

As slopes of both the lines are equal, the lines are parallel.

Hence, the given statement is true.