All You Need to Know about Slopes of Parallel and Perpendicular Lines
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So many parallel and perpendicular lines all over the place, and none of them have been labeled. Which begs the question: whose lines are they, anyway?
|Algebra||Real Numbers and Quantities|
|Geometry||Parallel and Perpendicular Lines|
|Mathematics and Statistics Assessment||Plane Geometry|
|Plane Geometry||Plane figures (triangles, rectangles, parallelograms, trapezoids, circles, polygons)|
The equations of their magic rays are: y=3x+4 and y=3x+10. [equations shown]
Fortunately, these equations are already set up in slope-intercept form (y=mx+b, where [equations on slopes]
m is the slope). [slope-intercept form demonstrated]
That means that the slope in each equation is 3.
According to the Magician's Apprentice Handbook, "If two lines are perpendicular, their slopes [handbook opens]
are negative reciprocals of each other."
Negative reciprocals, when multiplied together, equal -1. [negative reciprocals defined]
3 x -1/3 = -1, so if one of the two equations had a slope of -1/3, then these two equations
would be perpendicular to each other. [perpendicular lines explained]
If two lines are parallel, their slopes are the same. [parallel lines defined]
Since we know each equation has a slope of 3, their slopes are parallel.
Oh, here it is, page 32... [handbook opens]
"Parallel magic rays deployed at the same time result in... bear."
Get rid of the evidence. [kids run from bear]