Slope is defined as the steepness of a line. This property has many real world practical applications for architects, engineers, builders, artists and video game developers. On this How to Find the Slope web page, you will learn how to calculate the slope of a line with various formulas.
Finding the Slope
In this video, patrickJMT takes you step by step through the process of finding the slope of a line using the two point formula. He goes through a visual example that shows the points plotted on a graph. You'll find that his teaching style is casual yet informative. The running time is 6:41.
Introduction
It will help to have a basic understanding of arithmetic and algebra to follow along with this tutorial. In this article, you will see the visual explanation of slope as well as see how to determine slope from the equation of a line and from two points on a line. You may want to use graph paper to plot points although it is optional.
Visual Representation
In the figure below, you have a ramp that is 2 meters tall and 6 meters long. To figure out the incline, you simply divide the height by the length. That means that the slope is 1/3 in this example.
Slope Figure
Determine Slope From the Equation of a Line
If you have a line in the standard form Ax + By = C, you can calculate the slope as m = -A/B.
- Example: x - 4y = 0
- m = -1/-4
- m = 1/4
Calculate Slope From Two Points on a Line
If you need to find the slope of a line that exists between two points, you use the formula: m = y2 - y1/x2 - x1 where (x1,y1) and (x2,y2) are points on the same line.
- Example: Points (2,2) and (6,7)
- m = (7 - 2)/(6-2)
- m = 5/4
References
Fast Facts
-
Fact:
Two lines are parallel if they have the same slope.
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Fact:
To determine if two lines are perpendicular to each other, multiply their slopes. If you get -1, they are perpendicular. Here's the formula: m1m2 = -1 where m1 is the slope of one line and m2 is the slope of another. It can also be looked at with the formulas: m1 = -(1/m2) or m2 = -(1/m1).
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Fact:
A line in the form y = C is horizontal while a line with the form x = C is vertical. Of course, both of these have a slope of 0.
