Proving Relationships of Parallel and Perpendicular Lines

The exercise states that Line $1$ passes through $(3,\text{-}5)$ and $(2,\text{-}1).$ Furthermore, it also states that Line $2$ passes through the points $(0,3)$ and $(1,7).$ The slopes of both lines are correctly calculated using the Slope Formula. $$\begin{array}{rl}\text{Line }1\text{:}& (3,\text{-}5)\text{ and }(2,\text{-}1)\Rightarrow \text{slope: }\text{-}4\\ \text{Line }2\text{:}& (0,3)\text{ and }(1,7)\Rightarrow \text{slope: }4\end{array}$$ The lines are not parallel because the slopes are not the same. To determine whether or not they are perpendicular, we multiply the slopes. $$\begin{array}{c}\text{-}4(4)=\text{-}16\end{array}$$ We see that the product of the slopes is not $\text{-}1.$ Therefore, the lines are not perpendicular. The error was thinking that, because the slopes are opposite, the lines were perpendicular. The conclusion should be that lines $1$ and $2$ are neither parallel nor perpendicular.