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{{ printedBook.courseTrack.name }} {{ printedBook.name }} Parallel lines have the same slope but different $y-$intercepts. Perpendicular lines have slopes that are opposite reciprocals of one another. Therefore, to determine if the lines are parallel, perpendicular, or neither, we first need to find their individual slopes using the Slope Formula.

Line | Points | $x_{2}−x_{1}y_{2}−y_{1} $ | Slope |
---|---|---|---|

$a$ | $(-1,4)&(5,6)$ | $5−(-1)6−4 $ | $31 $ |

$b$ | $(-1,1)&(3,2)$ | $3−(-1)2−1 $ | $41 $ |

$c$ | $(-3,-2)&(3,0)$ | $3−(-3)0−(-2) $ | $31 $ |

$d$ | $(1,6)&(3,-2)$ | $3−1-2−6 $ | $-4$ |

Lines $a$ and $c$ have the same slope, but different $y-$intercepts. Therefore, they are parallel. Meanwhile, the slopes of lines $b$ and $d$ are opposite reciprocals, so they are perpendicular.