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Parallel and Perpendicular Lines. How to use Algebra to find parallel and perpendicular lines. Parallel Lines. How do we know when two lines are parallel? Their slopes are the same! The slope is the value m in the equation of a line: y = mx + b. Example: Find the equation of the line that is: parallel to y = 2x + 1.
- Slope
- −0.5
We can determine from their equations whether two lines are parallel by comparing their slopes. If the slopes are the same and the y -intercepts are different, the lines are parallel. If the slopes are different, the lines are not parallel. Unlike parallel lines, perpendicular lines do intersect.
Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals. In other words, if \(m=\frac{a}{b}\), then \(m_{⊥}=−\frac{b}{a}\). To find an equation of a line, first use the given information to determine the slope. Then use the slope and a point on the line to find the equation using point-slope form.
Likewise, parallel lines become perpendicular when one line is rotated 90°. Parallel Curves. Curves can also be parallel when they keep the same distance apart (called "equidistant"), like railroad tracks. The red curve is parallel to the blue curve in both these cases:
Parallel lines are those that never intersect and are always the same distance apart. Perpendicular lines are those that always intersect each other at right angles. Perpendicular lines are denoted by the symbol ⊥. The symbol || is used to represent parallel lines.
All of the lines shown in the graph are parallel because they have the same slope and different y-intercepts. Lines that are perpendicular intersect to form a [latex]{90}^{\circ }[/latex] angle. The slope of one line is the negative reciprocal of the other.
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Jun 14, 2022 · Perpendicular lines cross each other at exactly one point, making a 90° angle (right angle) with each other. Like parallel lines, perpendicular lines exist in the same plane as each other (coplanar). The product of the slopes of two perpendicular lines is -1. Properties of Perpendicular Lines. In the same plane. Intersect at one point.
