Answer
The lines are parallel.
Work Step by Step
To determine if the two lines are parallel, perpendicular, or neither, we need to check the slopes of the two lines.
The first equation is already written in slope-intercept form, which is given by the formula:
$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
According to this formula, the slope for the first line $y = 6x + 2$ is $6$.
Let us find the slope of the second line. This line is in standard form, so we need to transform it into slope-intercept form to find the slope. The slope-intercept form is given by the formula:
$y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
First, we want to subtract $18x$ from each side of the equation to isolate the $y$ term on the left side of the equation:
$-3y = -18x + 15$
Divide each side by $-3$ to isolate $y$:
$y = \frac{-18}{-3}x + \frac{15}{-3}$
Simplify the fractions:
$y = 6x - 5$
The slope for the second equation is $6$.
The slopes for the two equations are the same; therefore, they are parallel lines.
