select all the equations that represent lines parallel to y = 6x + 2. y = -\\frac{1}{6}x + 7 y = 6x - 12 12x…

Explanation:

Step1: Recall slope - parallel line relationship

Parallel lines have the same slope. The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope. For the line $y = 6x+2$, the slope $m = 6$.

Step2: Analyze each equation

Equation 1: $y=-\frac{1}{6}x + 7$

The slope $m_1=-\frac{1}{6}\neq6$, so it is not parallel.

Equation 2: $y = 6x-12$

The slope $m_2 = 6$, so it is parallel.

Equation 3: Rewrite $12x-2y = 4$ in slope - intercept form

First, solve for $y$: $-2y=-12x + 4$, then $y = 6x-2$. The slope $m_3 = 6$, so it is parallel.

Equation 4: Rewrite $6y=-x - 1$ in slope - intercept form

$y=-\frac{1}{6}x-\frac{1}{6}$. The slope $m_4=-\frac{1}{6}\neq6$, so it is not parallel.

Equation 5: $y = 3x+2$

The slope $m_5 = 3\neq6$, so it is not parallel.

Answer:

$y = 6x-12$, $12x - 2y=4$