Answer
The two lines are neither parallel nor perpendicular.
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 written 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 $2x$ from each side of the equation to isolate the $y$ term on the left side of the equation:
$-5y = -2x + 0$
Divide each side by $-5$ to isolate $y$:
$y = \frac{-2}{-5}x$
Simplify the fraction by dividing the numerator and denominator by $-1$:
$y = \frac{2}{5}x$
The slope for the first equation is $\frac{2}{5}$.
Let us find the slope of the second line. This line is in point-slope form, so we need to transform it into slope-intercept form to find the slope.
We want to subtract $3$ from each side of the equation to isolate the $y$ term on the left side of the equation:
$y = \frac{5}{2}x - 3$
The slope for the second equation is $\frac{5}{2}$.
The slopes for the two equations are not the same; therefore, they are not parallel lines.
Let's check to see if they are perpendicular to one another by multiplying them together:
$\frac{2}{5}(\frac{5}{2})$
Multiply to simplify:
$\frac{10}{10}$
Divide the numerator by the denominator to simplify:
$1$
The product of the slopes is not $-1$; therefore, these lines are not perpendicular.
