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  1. Slope of parallel lines examples: Example 1: Consider two lines having the slope of 3 5. Their graph shows that they have the same rise over run ratio. These lines are parallel. Example 2: Consider the lines y = 2 x + 3 and y = 2 x − 5. These two lines have the same slope, 2. However they have different y-intercepts.

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  3. Therefore the slope of the parallel line is m = 2. Example 2: Find the equation of a line passing through (-1, 2) and the slope of a parallel line is 2/3. Solution: The given slope of the parallel line is m = 2/3, and hence the slope of this required line is also m = 2/3. The given point is (x1,y1) (x 1, y 1) = (-1, 2)

  4. Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals. In other words, if m = a b, then m ⊥ = − 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.

  5. If two coincident lines form a system, every point on the line is a solution to the system. Parallel. Lines in a plane that are parallel, do not intersect. Two lines are parallel if they have the same slope, or if they are vertical. If two parallel lines form a system, there are no solutions to the system. Intersect.

  6. Purplemath. Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel. Perpendicular lines are a bit more complicated. If you visualize a line with ...

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  8. Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane). Parallel Lines in greater depth. On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 ...

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