Question

the equation of line t is $y = \frac{-5}{6}x + \frac{7}{4}$. the equation of line u is $y = \frac{6}{5}x + \frac{7}{5}$. are line t and line u parallel or perpendicular?

parallel
perpendicular
neither

Explanation:

Step1: Recall slope conditions

For 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 \( t \): \( m_1 = -\frac{5}{6} \); Line \( u \): \( m_2=\frac{6}{5} \).

Step3: Check parallel/perpendicular

\( m_1
eq m_2 \) (not parallel). \( m_1 \cdot m_2 = -\frac{5}{6} \cdot \frac{6}{5}=-1 \) (perpendicular condition met).

Answer:

perpendicular