Parallel lines

Definition

Parallel lines are two lines in a plane that never intersect and are always equidistant from each other. They have the same slope but different y-intercepts.

5 Must Know Facts For Your Next Test

1. Parallel lines have identical slopes.
2. The equation of parallel lines can be written in the form $y = mx + b$, where $m$ is the same for both lines, but $b$ is different.
3. If two linear equations are given, they represent parallel lines if their slopes (coefficients of x) are equal.
4. In coordinate geometry, the distance between parallel lines can be determined using their y-intercepts.
5. Two vertical lines are also considered parallel as they do not intersect.

Review Questions

• How do you determine if two given linear equations represent parallel lines?
• What is the relationship between the slopes of two parallel lines?
• Can two vertical lines be considered parallel? Why or why not?

Related terms

Slope: A measure of the steepness of a line, usually denoted by $m$, calculated as the ratio of rise over run.

Y-intercept: The point where a line crosses the y-axis on a graph, represented by $b$ in the equation $y = mx + b$.

Perpendicular Lines: $\text{Lines that intersect at a right angle (90 degrees). The product of their slopes is } -1.$