Question

select whether the pair of lines is parallel, perpendicular, or neither. select choice need help?

Explanation:

Step1: Find the slope of line \(PQ\)

Let \(P(-2, 3)\) and \(Q(5, - 1)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m_{PQ}=\frac{-1 - 3}{5+2}=\frac{-4}{7}\)

Step2: Find the slope of line \(TU\)

Let \(T(-3,-1)\) and \(U(0,-3)\). Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
\(m_{TU}=\frac{-3 + 1}{0+3}=\frac{-2}{3}\)

Step3: Check the relationship between slopes

Parallel lines have equal slopes (\(m_1=m_2\)), perpendicular lines have slopes with \(m_1\times m_2=- 1\).
Since \(\frac{-4}{7}
eq\frac{-2}{3}\) and \(\frac{-4}{7}\times\frac{-2}{3}=\frac{8}{21}
eq - 1\)

Answer:

Neither