Question

determine if the lines are parallel, perpendicular, or neither
( l_1: 6x + y = 5 )
( l_2: y - 4x = -3 )
are the lines parallel, perpendicular, or neither?
(circ) perpendicular
(circ) parallel
(circ) neither

Explanation:

Step1: Rewrite Line 1 in slope-intercept form

Rearrange $6x + y = 5$ to $y = mx + b$:
$y = -6x + 5$
Slope $m_1 = -6$

Step2: Rewrite Line 2 in slope-intercept form

Rearrange $y - 6x = -1$ to $y = mx + b$:
$y = 6x - 1$
Slope $m_2 = 6$

Step3: Check parallel/perpendicular conditions

Parallel: $m_1 = m_2$? $-6
eq 6$, so not parallel.
Perpendicular: $m_1 \times m_2 = -1$? $(-6) \times 6 = -36
eq -1$, so not perpendicular.

Answer:

Neither