Here, our change in y, and then, we would define That point, our change in y, would be this, right over "change," so change in x, and I could alsoĬalculate the change in y, so this point going up to This distance right over here, change in x, the Greek letter delta, This point to this point, what is my change in x?" Well, my change in x would be
Out the slope of this line, I could pick two points, say that point and that point. Have our classic y axis in the vertical direction and x axis in the horizontal direction, and if I wanted to figure To review it on Khan Academy, but all it is, it'sĭescribing the rate of change of a vertical variable with respect to a horizontal variable, so for example, here I This notion again gives us Δ𝑦/Δ𝑥 as the slope.Īlready familiar with the idea of a slope of a line.
So it is natural that we would want to gauge how much change in the dependent variable is caused by a unit change in the independent variable because we have control over the independent variable whereas the dependent variable is determined by the independent variable, not by us directly. We have no control over its value – it is completely determined by 𝑥. This everyday definition gives us Δ𝑦/Δ𝑥 for slope.Īlso, in terms of a linear equation, 𝑥 is viewed as an independent variable, that is, the variable we have control over. A mountain is steeper (has a greater slope) if for every 1 meter you go forward your altitude increases by 10 meters than if for every 1 meter you go forward your altitude increases by 2 meters. There are two natural reasons as to why slope is Δ𝑦/Δ𝑥 instead of the reciprocal.įirst, in everyday language, we say that something is steep if it has a large slope such that a small change horizontally corresponds to a drastic (large) change vertically.
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