One line passes through the points
\[\blueD{(1,9)}\] and
\[\blueD{(4,-9)}\]. Another line passes through points
\[\greenD{(6,5)}\] and
\[\greenD{(8,-5)}\].
Are the lines parallel, perpendicular, or neither?
We can find the slopes of the two lines to determine their relationship.
For the first line passing through $\blueD{(1,9)}$ and $\blueD{(4,-9)}$, the slope is
\[\frac{y_2-y_1}{x_2-x_1}=\frac{-9-9}{4-1}=\frac{-18}{3}=-6.\]
The slope-intercept form of this line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept. Plugging in the coordinates of one point, $9=(-6)(1)+b$, we find that $b=3$. Therefore, the equation of this line is $y=-6x+3$.
For the second line passing through $\greenD{(6,5)}$ and $\greenD{(8,-5)}$, the slope is
\[\frac{y_2-y_1}{x_2-x_1}=\frac{-5-5}{8-6}=\frac{-10}{2}=-5.\]
The slope-intercept form of this line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept. Plugging in the coordinates of one point, $5=(-5)(6)+b$, we find that $b=25$. Therefore, the equation of this line is $y=-5x+25$.
The slopes of the two lines are $-6$ and $-5$. Since the slopes are not equal and not negative reciprocals, the lines are $\boxed{\text{neither parallel nor perpendicular}}$.