Question

line u has a slope of \\(\frac{3}{5}\\). line v has a slope of \\(\frac{3}{5}\\). are line u and line v parallel or perpendicular? parallel perpendicular neither

Explanation:

Step1: Recall slope rules for lines

For two lines in a plane, if their slopes (\(m_1\) and \(m_2\)) are equal, i.e., \(m_1 = m_2\), the lines are parallel. If the product of their slopes is \(- 1\) (i.e., \(m_1\times m_2=-1\)), the lines are perpendicular.
Here, slope of line \(u\) (\(m_u\)) is \(\frac{3}{5}\) and slope of line \(v\) (\(m_v\)) is \(\frac{3}{5}\). So \(m_u=m_v=\frac{3}{5}\).

Step2: Determine relation between lines

Since the slopes of line \(u\) and line \(v\) are equal, by the definition of parallel lines (lines with equal slopes are parallel in a plane, assuming they are not the same line, which is a special case but here we just check slope condition), the lines are parallel. The product of their slopes is \(\frac{3}{5}\times\frac{3}{5}=\frac{9}{25}
eq - 1\), so they are not perpendicular.

Answer:

parallel