Question

the equation of line t is ( y = \frac{-9}{7}x + 4 ). the equation of line u is ( y = \frac{-9}{7}x + \frac{2}{7} ). are line t and line u parallel or perpendicular? options: 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 \(m_1\times m_2=- 1\).

Step2: Identify slopes

Line \(t\): \(y=\frac{-9}{7}x + 4\), so \(m_1=-\frac{9}{7}\).
Line \(u\): \(y=\frac{-9}{7}x+\frac{2}{7}\), so \(m_2 = -\frac{9}{7}\).

Step3: Compare slopes

Since \(m_1=m_2=-\frac{9}{7}\), the lines have equal slopes.

Answer:

parallel