Slope Formula
Slope formula is used to describe the steepness, line, gradient, or grade of a direct line. The bigger slope value is the steeper incline indicates. The slope is defined as the ratio of the "rise" divided by the "run" between 2 points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any 2 points on the line. It's also every time the same thing as how many rises in one run.
Using calculus, one could calculate the slope of the tangent to a curve at a point.
The concept of slope, and much of this article, applies straightly to grades or gradients in geography and civil engineering.
Lesson Objective
This lesson shows you how the slope formula is derived and some visual examples on using it.
The slope of a line in the plane containing the x and y axes is generally represented by the letter m, and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between 2 distinct points on the line. This is described by the following equation:
(The delta symbol, "Δ", is commonly used in mathematics to mean "difference" or "change".)
Given 2 points (x1, y1) and (x2, y2), the change in x from one to the other is x2 - x1, while the change in y is y2 - y1. Substituting both quantities into the above equation obtains the following:
Scientific Definition: The rate at which an object accelerates on a distance versus time graph is shown. Calculated by Slope = Rise / Run of a graph. Since the y-axis is vertical and the x-axis is horizontal by convention, the above equation is often memorized as "rise over run", where Δy is the "rise" and Δx is the "run". Therefore, by convention, m is equal to the change in y, the vertical coordinate, divided by the change in x, the horizontal coordinate; that is, m is the ratio of the changes. This concept is fundamental to algebra, analytic geometry, trigonometry, and calculus.
Note that the way the points are chosen on the line and their order doesn't matter; the slope will be the same in each case. Other curves have "accelerating" slopes and one could use calculus to calculate such slopes.
Tip #1
Understand how the 'change in y' and 'change in x' are calculated. To recall them, you can watch the math video in the slope of a line lesson.
Tip #2
It is important to understand the slope formula before using it. You'll be more comfortable calculating using the formula once you have understood it.
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