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Slope - Concept

Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

One of the most important things to understand about lines is the slope. Slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate slope by dividing the change in the x-value between two points over the change in the y-value. In order to understand the importance of the definition of slope, one should understand how to interpret graphs and how to write an equation.

So, slope of a line is how we measure the steepness of a line, okay? So for this little into we have a point x1,y1 and another point x2,y2. We don't know what the coordinates are, for this example it doesn't really matter. What we're mostly concerned with is how we calculate the steepness of this line.
So slope, for reasons I do not understand is that the abbreviate with the letter m and how we find it is the change of y over the change of x. Now order does matter in this case. In that, if you do the y, the second coordinate first for the y's it has to be the same as for the x's. We could just as easily have, switched our y order but if we do that we also have to make sure we switch our x order, okay? This is often also referred to as, rise overrun cause you're really determining the change of the rise, how much you're going up and down, versus the change of the run, how much you're going side to side. You also could say this as, delta y over delta x, delta is just a symbol that means change, so you're basically talking about the change of y over the change of x. A number of different ways of our representing the exact same thing, change of y over change of x, the steepness of a line.

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