Parallel Lines
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Parallel lines are two lines that never intersect or cross each other. They have the same slope but different y-intercepts. Since the lines are always the same distance apart, they will never meet, regardless of how far they are extended.
Key Characteristics of Parallel Lines:
Same Slope: The lines have identical slopes. In slope-intercept form y = mx + b, the m (slope) values for both lines are equal.
Different y-Intercepts: The lines have different y-intercepts (b) in their equations, which means they are vertically offset from each other.
Example:
Consider the two equations:
y = 3x + 2
y = 3x - 4
Both lines have the same slope m = 3, but their y-intercepts are different: one has b = 2, and the other has b = -4.
Because the slopes are the same and the y-intercepts are different, the lines are parallel and will never intersect.
Graphically:
When you graph these two equations, you will see that the lines are parallel to each other, running in the same direction and never crossing.