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{{ printedBook.courseTrack.name }} {{ printedBook.name }} The exercise states that Line $1$ passes through $(3,-5)$ and $(2,-1).$ 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.
$Line1:Line2: (3,-5)and(2,-1)⇒slope:-4(0,3)-and(1,7)-⇒slope:-4 $
The lines are **not** parallel because the slopes are not the same. To determine whether or not they are perpendicular, we multiply the slopes.
$-4(4)=-16 $
We see that the product of the slopes is **not** $-1.$ 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.