Question

the equation of line d is $y = \frac{-23}{67}x - \frac{40}{15}$. the equation of line e is $y = \frac{-23}{67}x - \frac{33}{35}$. are line d and line e parallel or perpendicular?
parallel
perpendicular
neither

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.
For line \( d \): \( y=\frac{-23}{67}x-\frac{40}{15} \), so the slope \( m_d=\frac{-23}{67} \).
For line \( e \): \( y = \frac{-23}{67}x-\frac{33}{35} \), so the slope \( m_e=\frac{-23}{67} \).

Step2: Check parallel/ perpendicular conditions

• Parallel lines: Two lines are parallel if their slopes are equal (\( m_1 = m_2 \)). Here, \( m_d=m_e=\frac{-23}{67} \), so the slopes are equal.
• Perpendicular lines: Two lines are perpendicular if the product of their slopes is \(- 1\) (\( m_1\times m_2=-1 \)). Let's check the product: \( \frac{-23}{67}\times\frac{-23}{67}=\frac{529}{4489}

eq - 1 \), so they are not perpendicular.

Answer:

parallel