Question

1. line m is represented by $y = \frac{3}{5}x - 3$. match each equation to the term that accurately describes its relationship to line m.

$y = -1\frac{2}{3}x + 3$
$y = -0.6x + 3$
$y = 0.6x + 3$
perpendicular
neither parallel nor perpendicular
parallel

Explanation:

Step1: Recall slope rules

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

• Parallel if \( m_1 = m_2 \).
• Perpendicular if \( m_1 \times m_2 = -1 \) (or \( m_2 = -\frac{1}{m_1} \)).

Line \( m \): \( y = \frac{3}{5}x - 3 \), so \( m_1 = \frac{3}{5}=0.6 \).

Step2: Analyze \( y = -1\frac{2}{3}x + 3 \)

Convert \( -1\frac{2}{3} \) to improper fraction: \( -\frac{5}{3} \).
Check product: \( \frac{3}{5} \times (-\frac{5}{3}) = -1 \). So perpendicular.

Step3: Analyze \( y = -0.6x + 3 \)

\( m_2 = -0.6 = -\frac{3}{5} \).
Product: \( \frac{3}{5} \times (-\frac{3}{5}) = -\frac{9}{25}
eq -1 \), and \( -\frac{3}{5}
eq \frac{3}{5} \). So neither.

Step4: Analyze \( y = 0.6x + 3 \)

\( m_2 = 0.6=\frac{3}{5} \), which equals \( m_1 \). So parallel.

Answer:

• \( y = -1\frac{2}{3}x + 3 \): perpendicular
• \( y = -0.6x + 3 \): neither parallel nor perpendicular
• \( y = 0.6x + 3 \): parallel