Slope of a Line Formula

Formula of the slope is given by the ratio of change in the y coordinate to the change in the x coordinate, which can be written mathematically as

Slope = Change in y coordinate/Change in x coordinate = Δy/Δx

Slope of a Line

If the inclination of the line with a positive x-axis is θ, then the slope is given as follows:

m = tan θ

Slope of a Line

Slope of a Line is the measure of the steepness of a line a surface or a curve whichever is the point of consideration. The slope of a Line is a fundamental concept in the stream of calculus or coordinate geometry or we can say the slope of a line is fundamental to the complete mathematics subject. The understanding of slope helps us solve many problems in mathematics, physics, or engineering.

In this article, we will learn about the slope of a line in detail, slope of a straight line with its various methods of calculations, and also the equation for the slope of a line.

Table of Content

  • What is a Slope?
  • What is the Slope of a Line?
  • Slope of a Line Equation
  • How to Find Slope of a Line?
    • Calculation of Slope between Two Points
    • Calculation of Slopes from Graph
    • Calculation of Slope from Table
  • Positive and Negative Slope
  • Slopes of Different Lines
    • Slope of Horizontal Line
    • Slope of Vertical Line
    • Slope of Perpendicular Lines
    • Slope of Parallel Lines
  • Equation of Line in Slope Intercept Form

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What is a Slope?

In mathematics, the slope is the measure of the steepness of a line or a surface which means the slope of a line tells us how steep a line or surface is inclined with the positive x-axis. The higher the slope of a curve or a line, the greater the amount of steepness it will show in the graph. Generally, the slope is defined in two-dimensional coordinates as the ratio of the change in the y-coordinate with respect to the change in the x-coordinate....

What is the Slope of a Line?

Similar to the general slope, the slope of a line or the slope of a straight line is the measure of the steepness of a line and is mathematically given as the ratio of the change in the y-coordinate to the change in the x-coordinate of the line. Other than this mathematical interpretation, the slope has a physical interpretation that tells us about the line that is in which direction the line will tilt....

Slope of a Line Formula

Formula of the slope is given by the ratio of change in the y coordinate to the change in the x coordinate, which can be written mathematically as...

Slope of a Line Equation

The slope of a line is given by the equation...

How to Find Slope of a Line?

There are various methods to find the slope of any line, which can be used appropriately on the basis of the given conditions. These methods are:...

Positive and Negative Slope

A line is said to have a positive slope if it is making less than the right angle with the positive x-axis and a line is said to have a negative slope if it makes more than the right angle with the positive x-axis....

Slopes of Different Lines

There can be various different lines that can be named such as:...

Equation of Line in Slope Intercept Form

The equation of a line in the slope-intercept form is given as follows:...

Equation of Line Using Slope

If a line is passing through a point (x1, y1) and its slope is m, then the equation of a line is given as follows:...

Equation of Line in Normal Form

Equation of the line whose length of the perpendicular from the origin is p and the angle made by the perpendicular with the positive x-axis is given by α is given by:...

Angle between Two Lines

When two lines with slopes m1 and m2 intersect they form angles. The relation between the slope of the intersecting lines and the angle so formed is given as follows:...

Sample Problems on Slope of a Line

Problem 1: Find the slope of points (1,2) and (2,3)....

FAQs on Slope of a Line

What is the Slope of a Line?...