In normal terms, you can consider this as an “uphill” scenario. When moving from left to right, if the line has a positive slope, it means the line is moving upwards.Slope represents not just steepness it also effectively tells the direction.Mathematically, you can interpret slope in this way too: The change in y or the dependent variable with the unit change in x or the independent variable. The usual notation of the slope-intercept form of the line is : y=mx c, where m is the slope of the line, which we calculate by the formula or dy/dx, as it is popularly called in short. The slope-intercept form of the line is well known in linear algebra. Slope is an indispensable concept in linear algebra and to describe line gradients. Similarly, the demand and price curve also is slopy and shows how the two terms are related to one another. For instance, the famous Philips curve that shows the variation of unemployment and inflation is a downward sloping curve. EconomicsĮconomists use the concept of slope to show how things are changing. The slope of a landform plays a key role in Geographic Information Systems (GIS) to analyze elevation points, to stimulate and design elevation models and to study contour lines. Geographers understand and classify soils, differentiate landforms and study the model surface runoff Water runoff is a determining factor to estimate which crops suit well that landforms and the cost of farming and measures to be taken for better productivity. However, there exist many pros and cons because of the slope. Hill stations and steep landforms offer a great sight to the viewers. Laying of roads and allotting permissions for vehicles in such places is based on such studies only. These are all nothing but the signs that alert you that the road ahead is steep and that you should drive carefully. You must also have noticed road signs showing “Steep Hill Ahead” or “20% with a steep triangle image”. We come across ups and downs and steep areas many times during our journeys or in day to day life too. It is a common sight to all of us that land is never in a straight form. Before we get into the calculation of slope, it is hence important to understand the diversified usage of slope in various aspects of our life. The perpendicular line formula to get directly the slope of the line that is perpendicular line.Though we all know slope as a mathematical concept, it is increasingly used in many applications of physics, geographical studies, and sports. If you want to make things more direct, use this perpendicular slope calculator and use Then, solving for \(y\), by dividing both sides of the equation by \(3\), the following is obtained Putting \(y\) on the left hand side and \(x\) and the constant on the right hand side we get We have been provided with the following equation: Solution: We first get the slope intercept equation for the GIVEN line, if possible Find the equation of the perpendicular line that passes through \((1, 1)\). Example of the calculation of a perpendicular line for a given line:Ĭonsider the line with equation \(2x 3y = 5)\). Typically, you will provide a point on the original line, where you want the Line, you need to provide one point where the line passes through. In order to identify one specific perpendicular Once you have a line, there is not one but many (infinite) perpendicular lines to the given line. Can you calculate the perpendicular line with no points The perpendicular line to a vertical line is a horizontal line. What is the perpendicular line of a vertical line The perpendicular line to a horizontal line is a vertical line. What is the perpendicular line of a horizontal line Once you have the slope of the given line, you use the formula for the perpendicular slope, by multiplying by minus one the Ultimately, if you define your given line with an equation, you need to get that equation into the slope-intercept form, so to get the slope. Otherwise, perhaps you have two points where the line passes through, in which case you can compute If you are provided with the slope and intercept to define the line The step is to find the slope of the given line. How do you find the perpendicular line of a line? In order to find that one you are looking for, you need to fixĪ point it passes through. Observe that one given line has infinite perpendicular lines to it. Slopes are defined, for the lines to be perpendicular, which is that the product of the slopes is -1. There is a specific condition for the slope and the perpendicular slope, whenever the Perpendicular lines are lines that cross forming a right angle. Lines where the slope is undefined (negative or positive infinity). Horizontal lines are lines with slope equal to zero, an vertical lines are Lines are in big part determined by their slope (inclination). Learn more about this perpendicular line calculator.
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