Parallel

Definition

Parallel lines are two or more lines in a plane that never intersect. They have the same slope but different y-intercepts.

5 Must Know Facts For Your Next Test

1. Parallel lines share the same slope.
2. The equation of a line parallel to a given line can be found by keeping the slope the same and changing the y-intercept.
3. In coordinate geometry, parallel lines remain equidistant from each other at all points.
4. If two linear equations result in parallel lines, they will have no solutions because they do not intersect.
5. The symbol for indicating that two lines are parallel is $\parallel$.

Review Questions

• What must be true about the slopes of two parallel lines?
• How do you determine if two linear equations represent parallel lines?
• If given the equation $y = 2x + 3$, what is an example of an equation of a line parallel to it?

Related terms

Slope: The measure of steepness or incline of a line, typically represented as 'm' in the equation $y = mx + b$.

Y-Intercept: The point where a line crosses the y-axis, represented as 'b' in the equation $y = mx + b$.

Perpendicular Lines: Two lines that intersect at a right angle (90 degrees). Their slopes are negative reciprocals of each other.