Question

the equation of line f is $y = \frac{3}{8}x + 6$. the equation of line g is $y = \frac{-8}{3}x + \frac{5}{9}$. are line f and line g parallel or perpendicular?
parallel
perpendicular
neither
submit

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 \(f\) has slope \(m_1=\frac{3}{8}\), line \(g\) has slope \(m_2 = \frac{-8}{3}\).

Step2: Check product of slopes

Calculate \(m_1\times m_2=\frac{3}{8}\times\frac{-8}{3}\).
Simplify: \(\frac{3\times(-8)}{8\times3}=- 1\).

Answer:

perpendicular