Question

the equation of line d is $y = \frac{-2}{9}x + 4$. the equation of line e is $y = \frac{9}{2}x + 1$. are line d and line e parallel or perpendicular?
parallel
perpendicular
neither
submit

Explanation:

Step1: Recall slope rules

For two lines \( y = m_1x + b_1 \) and \( y = m_2x + b_2 \), parallel lines have \( m_1 = m_2 \), perpendicular lines have \( m_1 \times m_2=- 1 \).

Step2: Identify slopes

Line \( d \): \( m_1=\frac{-2}{9} \), Line \( e \): \( m_2 = \frac{9}{2} \).

Step3: Check product of slopes

Calculate \( m_1\times m_2=\frac{-2}{9}\times\frac{9}{2}=- 1 \).

Answer:

perpendicular