Math 1 · Unit 4 · Lesson 1 · part 2 of 6
Parallel means the same slope
Parallel lines are lines that never cross.
Parallel means the same slope
Parallel lines are lines that never cross. They stay the same distance apart forever, like the two rails of a train track. On a graph, that happens for exactly one reason: the two lines have the same slope, the same steepness and the same direction, so neither one can ever catch up to the other. What is different is where they start: same m, different b.
This is the family idea again. In Unit 3, Lesson 3, changing b slid a line straight up or down without tilting it. Every slide gives a parallel line. Parallel lines are the members of the line family that share the same m and differ only in b: the same line, moved.
ParallelSame slope, different y-intercept. Never cross.
Not parallelDifferent slopes. Somewhere, they cross.
The same lineSame slope and same y-intercept. Not two lines at all, one line written twice (Lesson 3 makes this precise).