Question Video: Determining the Relation between Two Lines Using Their Equations Mathematics • 11th Grade

Determine whether the lines 𝑦 = (−1/7)𝑥 − 5 and 𝑦 = (−1/7)𝑥 − 1 are parallel, perpendicular, or neither.

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Video Transcript

Determine whether the lines 𝑦 equals negative one-seventh 𝑥 minus five and 𝑦 equals negative one-seventh 𝑥 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 we’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 𝑦 equals 𝑚𝑥 plus 𝑏. In both cases, the coefficient of 𝑥 — the 𝑚 variable — is negative one-seventh. The 𝑚 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, “parallel lines have the same slope.” 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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