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 Amsco Integrated Algebra I: The Slopes of Parallel and Perpendicular Lines
This is a free lesson from our course in Amsco's Integrated Algebra
This lesson explains basics of the slope or gradient of parallel and perpendicular lines. Following this, it illustrates with the help of several examples and their solutions how to find the slope of parallel and perpendicular lines. The higher the slope of a graph at a point, the steeper the line is at that point. A negative slope means that the line slopes downwards. To find the slope of a straight-line graph, you’ll find it is often useful to find out what the gradient of a graph is. For a straight-line graph, pick two points on the graph. The slope of the line = (change in y-coordinate)/(change in x-coordinate) . (More text below video...)
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(Continued from above)
Moving forward, to find slope of parallel lines- say l1 and l2 are two parallel lines and m1 is slope of line l1 and m2 is the slope of line l2, then m1 = m2. Further on, to find the slope of perpendicular lines l1 and l2 the statement is true i.e. “if the slope of l1 is m1, the slope of l2 is m2, and l1 is perpendicular to l2, then m1 • m2 = -1”.
For example: two lines are parallel if they have the same slope. Say lines y = 3x + 1 and y = 3x + 4 are parallel, because both have a slope of 3. If two lines are perpendicular i.e. if one is at right angles to another, then their slopes when multiplied together will give -1. Say you need to find the equation of a line perpendicular to y = 4 - 3x. You’ll see this line has slope -3. A perpendicular line shall have a slope of 1/3, as (-3) x (1/3) = -1. Any line with gradient 1/3 will be perpendicular to this line i.e. y = (1/3) x.
The video above explains in detail with the help of several examples.

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