Question

decide whether the pair of lines is parallel, perpendicular, or neither.\\( l_1: 2x + 4y = 1 \\)\\( l_2: 4x + 2y = 4 \\)\
choose the correct answer below.\
\\( \bigcirc \\) a. the lines are perpendicular.\
\\( \bigcirc \\) b. the lines are parallel.\
\\( \bigcirc \\) c. the lines are neither parallel nor perpendicular.

Explanation:

Step1: Convert $L_1$ to slope-intercept form

Rearrange $2x + 4y = 1$ to solve for $y$:
$4y = -2x + 1$
$y = \frac{-2}{4}x + \frac{1}{4}$
$y = -\frac{1}{2}x + \frac{1}{4}$
Slope of $L_1$, $m_1 = -\frac{1}{2}$

Step2: Convert $L_2$ to slope-intercept form

Rearrange $4x + 2y = 4$ to solve for $y$:
$2y = -4x + 4$
$y = \frac{-4}{2}x + \frac{4}{2}$
$y = -2x + 2$
Slope of $L_2$, $m_2 = -2$

Step3: Check parallel/ perpendicular conditions

• Parallel lines have equal slopes: $m_1

eq m_2$ ($-\frac{1}{2}
eq -2$), so not parallel.

• Perpendicular lines satisfy $m_1 \times m_2 = -1$:

$m_1 \times m_2 = -\frac{1}{2} \times (-2) = 1
eq -1$, so not perpendicular.

Answer:

C. The lines are neither parallel nor perpendicular.