Question

determine if the lines are para
5.
$y = \frac{5}{3}x - 4$
$y = \frac{3}{5}x + 5$
$m_1 = \underline{\quad\quad}$
$m_2 = \underline{\quad\quad}$
$\parallel$ $\perp$ neither

Explanation:

Step1: Identify slope of first line

For $y = \frac{5}{3}x - 4$, slope $m_1 = \frac{5}{3}$

Step2: Identify slope of second line

For $y = \frac{3}{5}x + 5$, slope $m_2 = \frac{3}{5}$

Step3: Check parallel condition

Parallel lines have equal slopes: $\frac{5}{3}
eq \frac{3}{5}$, so not parallel.

Step4: Check perpendicular condition

Perpendicular lines have slopes with product $-1$:
$\frac{5}{3} \times \frac{3}{5} = 1
eq -1$, so not perpendicular.

Answer:

$m_1 = \frac{5}{3}$
$m_2 = \frac{3}{5}$
neither