Parallel Lines
Parallel lines are a pair of lines in a plane that do not intersect each other, no matter how far they are extended
Parallel lines are a pair of lines in a plane that do not intersect each other, no matter how far they are extended. The key characteristic of parallel lines is that they have the same slope.
To determine if two lines are parallel, you need to compare their slopes. The slope of a line is determined by the ratio of the change in y-coordinates to the change in x-coordinates between any two points on the line. If two lines have the same slope, they are parallel.
For example, let’s consider two lines with equations y = 2x + 3 and y = 2x – 1. Both lines have a slope of 2, meaning they have the same steepness and direction. Therefore, these lines are parallel.
On the other hand, if you have two lines with different slopes, they will never be parallel. For instance, if the equations of two lines are y = 2x + 3 and y = 3x – 1, their slopes are 2 and 3, respectively. Since the slopes are different, the lines will never be parallel.
It is also important to note that two lines can be parallel even if they are not in the same position on the coordinate plane. For example, if you have the lines y = 2x + 3 and y = 2x + 7, although they are not coincident, they still have the same slope of 2 and are therefore parallel.
In summary, to determine if two lines are parallel, compare their slopes. If the slopes are the same, the lines are parallel. If the slopes are different, the lines are not parallel.
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