Question

the equation of line a is $y = \frac{3}{4}x + 2$. the equation of line b is $y = \frac{-4}{3}x + 9$. are line a and line b parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Recall slope rules

For two lines \( y = m_1x + b_1 \) and \( y = m_2x + b_2 \):

• Parallel if \( m_1 = m_2 \).
• Perpendicular if \( m_1 \cdot m_2 = -1 \).

Step2: Identify slopes

Line \( a \): \( y = \frac{3}{4}x + 2 \), so \( m_1 = \frac{3}{4} \).
Line \( b \): \( y = \frac{-4}{3}x + 9 \), so \( m_2 = \frac{-4}{3} \).

Step3: Check product of slopes

Calculate \( m_1 \cdot m_2 \):
\( \frac{3}{4} \cdot \frac{-4}{3} = -1 \).

Answer:

perpendicular