Question

the equation of line $j$ is $y = \frac{7}{4}x + \frac{5}{3}$. the equation of line $k$ is $y = \frac{-4}{7}x + 8$. are line $j$ and line $k$ parallel or perpendicular?
parallel perpendicular neither

Explanation:

Step1: Identify slopes of lines

Slope of line $j$: $m_j = \frac{7}{4}$; Slope of line $k$: $m_k = \frac{-4}{7}$

Step2: Check parallel condition

Parallel lines have equal slopes: $\frac{7}{4}
eq \frac{-4}{7}$, so not parallel.

Step3: Check perpendicular condition

Perpendicular lines satisfy $m_j \times m_k = -1$:
$\frac{7}{4} \times \frac{-4}{7} = -1$

Answer:

perpendicular