Question

determine if the equations represent parallel lines, perpendicular lines, or neither.
$l_1: y = -3x + 3$
$l_2: y = \frac{1}{3}x - 1$
the lines are select

Explanation:

Step1: Recall slope properties

For two lines \( y = m_1x + b_1 \) and \( y = m_2x + b_2 \):

• Parallel: \( m_1 = m_2 \)
• Perpendicular: \( m_1 \times m_2 = -1 \)

Step2: Identify slopes

Line \( l_1 \): \( y = -3x + 3 \), so \( m_1 = -3 \)
Line \( l_2 \): \( y = \frac{1}{3}x - 1 \), so \( m_2 = \frac{1}{3} \)

Step3: Check parallel

\( -3
eq \frac{1}{3} \), not parallel.

Step4: Check perpendicular

Multiply slopes: \( (-3) \times \frac{1}{3} = -1 \)

Answer:

perpendicular