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If you look at train tracks stretching toward the horizon, the two steel rails never crash into each other. But look at a window frame or a street intersection, and the lines meet at crisp 90β square corners.
In algebra, a single number controls both behaviors: the slope (m), which measures the steepness or ratio of vertical change (rise) to horizontal change (run).
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How can you tell whether two lines will run side-by-side forever without ever drawing a single graph?
Parallel Lines
Parallel lines are lines in the same flat plane that never intersect, no matter how far you extend them.
Because they climb or descend at the exact same rate, non-vertical parallel lines always have the same slope (m1β=m2β) but different y-intercepts (b1βξ =b2β).
πInteractive diagram
Consider the equations y=β52βx+6 and 2x+5y=10. Rewriting the second equation into slope-intercept form gives y=β52βx+2.
Since both slopes are β52β and their y-intercepts (6 and 2) are different, the lines are strictly parallel.
What happens if two lines do cross, but meet at an exact, perfect right angle?
Perpendicular Lines
Perpendicular lines are lines that intersect to form a 90β right angle.