Question

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

neither
parallel
perpendicular

Explanation:

Step1: Convert lines to slope-intercept form

Slope-intercept form: $y=mx+b$, where $m$ is slope.

• For $4y=2x-4$: $y=\frac{2}{4}x-\frac{4}{4}$ → $y=\frac{1}{2}x-1$, slope $m_1=\frac{1}{2}$
• For $y=-2x+9$: slope $m_2=-2$
• For $y=2x+4$: slope $m_3=2$
• For $2y=4x-7$: $y=\frac{4}{2}x-\frac{7}{2}$ → $y=2x-\frac{7}{2}$, slope $m_4=2$
• For $2y=4x+4$: $y=\frac{4}{2}x+\frac{4}{2}$ → $y=2x+2$, slope $m_5=2$
• For $y=-2x-2$: slope $m_6=-2$

Step2: Check parallel (equal slopes)

Parallel lines have identical slopes:

• $y=2x+4$ ($m=2$) and $2y=4x-7$ ($m=2$)
• $2y=4x+4$ ($m=2$) and $y=-2x-2$ is not parallel; $2y=4x+4$ ($m=2$) pairs with $y=2x+4$ / $2y=4x-7$, and $y=-2x+9$ ($m=-2$) pairs with $y=-2x-2$ ($m=-2$)

Step3: Check perpendicular (product=-1)

Perpendicular slopes: $m_1 \times m_2 = -1$

• $\frac{1}{2} \times (-2) = -1$, so $4y=2x-4$ and $y=-2x+9$ are perpendicular

Step4: Check neither (no slope match)

No remaining pairs; confirm all are categorized.

Answer:

• Parallel: $y=2x+4$ and $2y=4x-7$; $2y=4x+4$ and $y=-2x-2$ is not, correct parallel pairs: $y=2x+4$ & $2y=4x-7$, $2y=4x+4$ & $y=2x+4$, $y=-2x+9$ & $y=-2x-2$
• Perpendicular: $4y=2x-4$ and $y=-2x+9$
• Neither: (No remaining pairs; all pairs are categorized above)

Corrected precise pairing:

1. Parallel:

• $y=2x+4$ and $2y=4x-7$
• $2y=4x+4$ and $y=2x+4$
• $y=-2x+9$ and $y=-2x-2$

1. Perpendicular:

• $4y=2x-4$ and $y=-2x+9$

1. Neither:

• (No uncategorized line pairs left)