Question

1. if i am looking for a line parallel to $y = -3x - 2$ which one of these equations could it be?

a $y = -2x - 3$\t\t\tb $y = -3x + 6$
c $y = -2x - 1$\t\t\td $y = 3x - 4$

1. $y = \frac{-2}{3}x + 2$ and $y = \frac{3}{2}x + 9$ are what kind of lines?

a perpendicular\t\t\tb parallel
c neither

1. write the equation of a line parallel to $y = 2x + 3$ that passes through the point (3, 1).

a $y = 2x - 5$\t\t\tb $y = 2x - 3$
c $y = -\frac{1}{2}x + \frac{5}{2}$\t\t\td $y = 2x + 1$

Explanation:

Step1: Identify parallel line rule

Parallel lines have equal slopes ($m_1=m_2$) in $y=mx+b$.

Step2: Solve Q1: Match slope

Given $y=-3x-2$, slope $m=-3$. Option B: $y=-3x+6$ has $m=-3$.

Step3: Solve Q2: Check line relationship

For $y=\frac{-2}{3}x+2$ ($m_1=\frac{-2}{3}$) and $y=\frac{3}{2}x+9$ ($m_2=\frac{3}{2}$):
$\frac{-2}{3} \times \frac{3}{2} = -1$. Perpendicular lines have $m_1 \times m_2=-1$.

Step4: Solve Q3: Find parallel line equation

Parallel to $y=2x+3$, so $m=2$. Use point $(3,1)$ in $y=mx+b$:
$1=2(3)+b \implies 1=6+b \implies b=1-6=-5$. Equation: $y=2x-5$.

Answer:

1. B. $y = -3x + 6$
2. A. Perpendicular
3. A. $y = 2x - 5$