Determine if lines $L _ { 1 }$ and $L _ { 2 }$ are parallel, perpendicular, or neither. $L _ { 1 } : 4 x - 4 y = - 4$ $L _ { 2 } : 8 x + 8 y = 9$
A)parallel
B)neither
C)perpendicular

Question

Quizplus · Accepted Answer

To determine the relationship between the two lines, we first convert their equations into slope-intercept form (y = mx + b), where m is the slope. For $L_1: 4x - 4y = -4$, dividing the entire equation by 4 gives $x - y = -1$ or $y = x + 1$, so the slope $m_1 = 1$. For $L_2: 8x + 8y = 9$, dividing the entire equation by 8 gives $x + y = \frac{9}{8}$ or $y = -x + \frac{9}{8}$, so the slope $m_2 = -1$. Since the slopes are negative reciprocals of each other ($m_1 = -1/m_2$), the lines are perpendicular.

Determine If Lines L1L _ { 1 }L1​ And L2L _ { 2 }L2​

Determine If Lines $L _ { 1 }$ And $L _ { 2 }$