All You Need to Know about Slopes of Parallel and Perpendicular Lines
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]