Question

given equations

1. $y = 7x + 2$ and $y = 7x - 1$
2. $y = \frac{4}{5}x - 8$ and $y = -\frac{5}{4}x + 3$
3. $y = -\frac{1}{3}x + 2$ and $y = \frac{1}{3}x$
4. $x + 6y = 30$ and $3y = 18x - 6$
5. $5x - y = 4$ and $y = -\frac{1}{5}x + 7$
6. $3x - y = 2$ and $12x - 4y = 4$
7. $y = x + 3$ and $y = -x - 5$
8. $y = 6$ and $x = -1$

$-4-4=-8$ neither

Explanation:

Key Rules:

• Parallel Lines: Have equal slopes ($m_1=m_2$)
• Perpendicular Lines: Slopes multiply to $-1$ ($m_1 \times m_2 = -1$)
• First convert all equations to slope-intercept form $y=mx+b$ to identify slope $m$.

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Problem 9

Step1: Identify slopes of both lines

For $y=7x+2$, $m_1=7$; for $y=7x-1$, $m_2=7$

Step2: Compare slopes

$m_1=m_2=7$

Answer:

(9): Parallel

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Problem 10

Step1: Identify slopes of both lines

For $y=\frac{4}{5}x-8$, $m_1=\frac{4}{5}$; for $y=-\frac{5}{4}x+3$, $m_2=-\frac{5}{4}$

Step2: Check perpendicularity

$m_1 \times m_2 = \frac{4}{5} \times -\frac{5}{4} = -1$