Question

line q has a slope of \\(\frac{56}{53}\\). line r has a slope of \\(\frac{-54}{24}\\). are line q and line r parallel or perpendicular?
parallel perpendicular neither
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Explanation:

Step1: Recall slope conditions

For parallel lines, slopes are equal. For perpendicular lines, the product of slopes is \(-1\). Let \(m_q=\frac{56}{53}\) and \(m_r = \frac{- 54}{24}\).

Step2: Check parallel

Compare \(m_q\) and \(m_r\). \(\frac{56}{53}
eq\frac{-54}{24}\), so not parallel.

Step3: Check perpendicular

Calculate \(m_q\times m_r=\frac{56}{53}\times\frac{-54}{24}=\frac{56\times(- 54)}{53\times24}=\frac{-3024}{1272}\approx - 2.377
eq - 1\). So not perpendicular.

Answer:

neither