Question

1
drag the tiles to the correct boxes to complete the pairs.
determine whether each pair of lines is perpendicular, parallel, or neither.
$y = 2x + 4$
$2y = 4x - 7$
$4y = 2x - 4$
$y = -2x + 9$
$2y = 4x + 4$
$y = -2x - 2$
neither
perpendicular
parallel

Explanation:

Step1: Recall slope rules

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

• Parallel: \(m_1 = m_2\) (and \(b_1

eq b_2\) to avoid coinciding).

• Perpendicular: \(m_1 \cdot m_2 = -1\).
• Neither: Otherwise.

Step2: Analyze first pair (\(y = 2x + 4\); \(2y = 4x - 7\))

Rewrite \(2y = 4x - 7\) as \(y = 2x - \frac{7}{2}\).
Slopes: \(m_1 = 2\), \(m_2 = 2\). \(m_1 = m_2\) → Parallel.

Step3: Analyze second pair (\(4y = 2x - 4\); \(y = -2x + 9\))

Rewrite \(4y = 2x - 4\) as \(y = \frac{1}{2}x - 1\).
Slopes: \(m_1 = \frac{1}{2}\), \(m_2 = -2\).
Check product: \(\frac{1}{2} \cdot (-2) = -1\) → Perpendicular.

Step4: Analyze third pair (\(2y = 4x + 4\); \(y = -2x - 2\))

Rewrite \(2y = 4x + 4\) as \(y = 2x + 2\).
Slopes: \(m_1 = 2\), \(m_2 = -2\).
Product: \(2 \cdot (-2) = -4
eq -1\); Slopes not equal → Neither.

Answer:

• Parallel: \(y = 2x + 4\) and \(2y = 4x - 7\)
• Perpendicular: \(4y = 2x - 4\) and \(y = -2x + 9\)
• Neither: \(2y = 4x + 4\) and \(y = -2x - 2\)