Question

the equation of line m is $y = \frac{-7}{3}x + 9$. the equation of line n is $y = \frac{3}{7}x + 9$. are line m and line n parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Recall slope properties

For two lines \(y = m_1x + b_1\) and \(y = m_2x + b_2\), parallel lines have \(m_1 = m_2\), perpendicular lines have \(m_1\times m_2=- 1\).
Line \(m\) has slope \(m_1=\frac{-7}{3}\), line \(n\) has slope \(m_2 = \frac{3}{7}\).

Step2: Check parallel condition

Compare \(m_1\) and \(m_2\). \(\frac{-7}{3}
eq\frac{3}{7}\), so not parallel.

Step3: Check perpendicular condition

Calculate \(m_1\times m_2=\frac{-7}{3}\times\frac{3}{7}=- 1\).

Answer:

perpendicular