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Linear functions, parallel and perpendicular Explained clearly

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Published on Oct 15, 2024

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It is explained in an understandable way when linear functions are parallel and perpendicular. The special features and rules for this are discussed both graphically and in terms of the functional equations. The general form of the functional equation of a linear function is f(x) = mx + b, where m is the slope and b is the y-axis intercept. If two linear functions are parallel, the lines must have the same slope. The y-axis intercept of the line is irrelevant for parallelism. In order to set up the functional equation of a parallel line (linear function), the slope must be chosen to be the same and the y-axis intercept can be set arbitrarily. If the parallel line is also to run through a certain, given point, b (i.e. the y-axis intercept) must be found accordingly. For two linear functions that are perpendicular to each other (the lines are at right angles to each other), the two slopes must be multiplied together to give -1. With this formula or equation you can check whether two linear functions are perpendicular to each other and also set up or find out a desired perpendicular linear function. The y-axis intercept is irrelevant when it comes to the question of whether two lines are perpendicular to each other. I will explain the whole topic to you in an understandable way using examples.

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