Video: Determining the Relation between Two Lines Using Their Equations

Determine whether the lines ๐‘ฆ = (โˆ’1/7)๐‘ฅ โˆ’ 5 and ๐‘ฆ = (โˆ’1/7)๐‘ฅ โˆ’ 1 are parallel, perpendicular, or neither.

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Video Transcript

Determine whether the lines ๐‘ฆ equals negative one-seventh ๐‘ฅ minus five and ๐‘ฆ equals negative one-seventh ๐‘ฅ minus one are parallel, perpendicular, or neither.

The categories parallel, perpendicular, or neither are always, we categorize, intersections of lines. Parallel lines do not intersect. Perpendicular lines intersect at a 90-degree angle. The category neither here represents all the lines that do intersect but do not form a 90-degree angle. Parallel, perpendicular, or neither.

But weโ€™re not given a graph for these two lines. Of course, we could try and draw a graph for both of these lines. But we can determine parallel, perpendicular, or neither without graphing these two equations. Both of these straight lines are given in the form ๐‘ฆ equals ๐‘š๐‘ฅ plus ๐‘. In both cases, the coefficient of ๐‘ฅ โ€” the ๐‘š variable โ€” is negative one-seventh. The ๐‘š variable represents the slope. And so, we can say that the slope of line one is negative one-seventh and the slope of line two is negative one seventh, which reminds us, โ€œparallel lines have the same slope.โ€ That is why they do not intersect. Since both of these lines have a slope of negative one-seventh, we can classify them as parallel lines without graphing.

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