Question

the equation of line s is $y = \frac{7}{5}x + \frac{1}{3}$. the equation of line t is $y = \frac{5}{7}x + 1$. are line s and line t 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 \(m_1\times m_2=- 1\).
Slope of line \(s\) (\(m_1\)) is \(\frac{7}{5}\), slope of line \(t\) (\(m_2\)) is \(\frac{5}{7}\).

Step2: Check parallel condition

Compare \(m_1\) and \(m_2\). \(\frac{7}{5}
eq\frac{5}{7}\), so not parallel.

Step3: Check perpendicular condition

Calculate \(m_1\times m_2\): \(\frac{7}{5}\times\frac{5}{7} = 1
eq - 1\), so not perpendicular.

Answer:

neither