Answer
neither
Work Step by Step
To determine if two lines are perpendicular, parallel, or neither, we need to look at their slopes.
Perpendicular lines have slopes that are negative reciprocals of one another. Parallel lines have the same slope.
The lines given are in standard form, but we want them in slope-intercept form so we can locate the slope easily. The slope-intercept form is given by the formula:
$y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept.
For the equation $2x - 3y = 1$, we first subtract $2x$ from each side of the equation to isolate the $y$ term on the left side of the equation:
$-3y = -2x + 1$
$y = \frac{2}{3}x - \frac{1}{3}$
We can see that the slope of this line is $\frac{2}{3}$.
Consider the second equation:
$-2y = -3x + 8$
Divide each side by $-2$ to isolate $y$:
$y = \frac{3}{2}x - 4$
We can see that the slope of this line is $\frac{3}{2}$.
The slopes are neither the same nor negative reciprocals of one another; therefore, these lines are neither parallel nor perpendicular.
