Question

determine if the lines are parallel, perpendicular, or neither.
l₁: 5x = 4y + 32
l₂: -8y = 10x - 32

are the lines parallel, perpendicular, or neither?
○ perpendicular
○ parallel
○ neither

Explanation:

Step1: Rewrite L1 in slope-intercept form

Isolate $y$ for $5x = 4y + 32$:
$4y = 5x - 32$
$y = \frac{5}{4}x - 8$
Slope of $L_1$, $m_1 = \frac{5}{4}$

Step2: Rewrite L2 in slope-intercept form

Isolate $y$ for $8y = 10x - 32$:
$y = \frac{10}{8}x - 4$
Simplify: $y = \frac{5}{4}x - 4$
Slope of $L_2$, $m_2 = \frac{5}{4}$

Step3: Compare slopes

Parallel lines have equal slopes; perpendicular lines have slopes that are negative reciprocals.
Here, $m_1 = m_2 = \frac{5}{4}$

Answer:

Parallel