Math 1 · Unit 4 · Lesson 3 · part 2 of 5
One decision, in order
Two lessons, one number.
One decision, in order
Two lessons, one number. Given any two lines, you can say how they are related by comparing their slopes. Here is the whole decision, in order.
- 1Get both slopesRead m off y = mx + b (rewrite first if needed), count rise over run on a graph, or subtract two points. Get both y-intercepts too if you can.
- 2Equal slopes?If the slopes match, check b. Different b: parallel. Same b too: it is the same line written twice.
- 3Negative reciprocals?Multiply the slopes. Product −1: perpendicular. (Horizontal and vertical: perpendicular by sight.)
- 4Otherwise: neitherDifferent slopes that do not multiply to −1. The lines cross, but not at a square corner.
Same lineSame m, same b. y = 2x + 1 and 4x − 2y = −2.
ParallelSame m, different b. y = 2x + 1 and y = 2x − 4.
PerpendicularSlopes multiply to −1. y = 2x + 1 and y = −12x + 6.
NeitherAnything else. y = 2x + 1 and y = 3x + 1 (they cross at (0, 1), but not squarely).
From two pairs of points. If each line is given by two points, find each slope as rise over run (second minus first, both times), then run the same decision. To tell same line from parallel when slopes match, check whether a point of one line satisfies the other line's equation.