Gradient Of a Line
The gradient of a line is defined as the change in the "y" coordinate with respect to the change in the "x" coordinate of that line. The gradient of a line is helpful to find the inclination or steepness of a line. The gradient of a line formula calculates the slope of any line by finding the ratio of the change in the yaxis to the change in the xaxis.
Let us learn more about the gradient of a line, how to find the gradient of a line, applications of gradient of a line, and the examples.
1.  What Is Gradient of a Line? 
2.  How To Find Gradient of a Line? 
3.  Applications of Gradient of a Line 
4.  Examples of Gradient of a Line 
5.  Practice Questions 
6.  FAQs on Gradient of a Line 
What Is Gradient of a Line?
The gradient of a line is used to calculate the steepness of a line and determines how much it is inclined with reference to the xaxis. To calculate the gradient of any line, the x and y coordinates of a line are used. In other words, it is the ratio of the change in the yaxis to the change in the xaxis.
The formula to calculate the gradient of a line is given as, m = (\(y_2\)−\(y_1\))/(\(x_2\)−\(x_1\)) = Δy/Δx, Where m represents the gradient of the line. \(x_1\), \(x_2\) are the coordinates of the xaxis, and \(y_1\), \(y_2\) are the coordinates of the yaxis. The x and y coordinates of the point are used to calculate the gradient of the line, which is also referred as the slope of the line.
The gradient of a line can also be measured as the net change in y coordinate with respect to the change in x coordinate and can be written as, m = Δy/Δx. Here, Δy is the change in ycoordinates, and Δx is the change in the xcoordinates. Also, we know that tan θ is also the slope of the line where θ is the angle made by the line with the positive direction of the xaxis, and, tanθ=height/base.Thus, the gradient of the line is, m=tanθ=Δy/Δx
How To Find Gradient of a Line?
The gradient of a line can be computed from the following below methods.
 From Two Points: The gradient of a line can be computed from any two points lying on the line. For the two points \((x_1, y_1)\), \((x_2, y_2)\), the gradient of the line is \(m = \dfrac{y_2  y_1}{x_2  x_1}\)
 Angle Of Inclination: The angle of inclination of the line is θ with respect to the xaxis. The gradient of a line is the value obtained from the tangent of the angle of inclination of the line with respect to the xaxis. m = Tanθ.
 Equation of a Line: The equation of a line is also helpful to find the gradient of a line. The standard form of the equation of a line, having the equation ax + by + c = 0, has a gradient of m = a/b. And the slopeintercept form of the equation of a line y = mx + c, has a gradient m, which is the coefficient of the x term.
Applications of Gradient of a Line
The gradient of a line has numerous applications in coordinate geometry, threedimensional geometry, and vector algebra. Some of the important applications of the gradient of a line are as follows.
 The gradient of a line gives the inclination of the line with respect to the xaxis.
 The gradient of a line is used to find the equation of a line.
 The gradient of a line has applications in threedimensional geometry, to find the equation of a line and the equation of a plane.
 The gradient of two lines is useful to find the angle between the two lines.
 The gradient of two lines is useful to know if the two lines are parallel or perpendicular with respect to each other.
 The product of the gradient of two perpendicular lines is equal to 1. \(m_1.m_2 = 1\).
 The gradient of two parallel lines is equal in value. \(m_1 = m_2\).
Related Topics
The following topics help in a better understanding of the gradient of a line.
Examples of Gradient of a Line

Example 1: Find the gradient of a line passing through the points (4, 5), and (2, 3)
Solution:
The two given points are \((x_1, y_1)\) = (4, 5), and \((x_2, y_2)\) = (2, 3).
The formula to find the gradient of the line is m = \(\dfrac{y_2  y_1}{x_2  x_1}\) = \(\dfrac{2  4}{3  (5)}\) = \(\dfrac{2}{8}\) = 1/4.
Therefore, the gradient of the line is m = 1/4.

Example 2: Find the gradient of a line having the equation 5x  4y + 11 = 0.
Solution:
The given equation of the line is 5x  4y + 11 = 0.
Comparing this equation with the equation of the line ax + by + c = 0, the gradient of the line is m = a/b.
Here for the given equation, we have a = 5, and b = 4.
The gradient of the line is m = (5)/4 = 5/4
Therefore, the gradient of the line is 5/4.
FAQs on Gradient of a Line
What Is Gradient of a Line?
The gradient of a line is the slope or inclination of the line with respect to the xaxis. The gradient of a line is given as, m = (\(y_2\)−\(y_1\))/(\(x_2\)−\(x_1\)) = Δy/Δx, Where m represents the gradient of the line. \((x_1, y_1)\). \((x_2, y_2)\) are any two points on the line..
How Do You Find Gradient of a Line?
The gradient of a line can be computed from any two points on the line, the angle of inclination of the line, or from the equations of the line. .
 For the two points \((x_1, y_1)\), \((x_2, y_2)\), the gradient of the line is \(m = \dfrac{y_2  y_1}{x_2  x_1}\)
 For the angle of inclination of the line 'θ' with respect to the xaxis, the gradient of a line is m = Tanθ.
 The standard equation of a line ax + by + c = 0, has the gradient of m = a/b.
 The slopeintercept form of the equation of a line y = mx + c, has a gradient m, which is the coefficient of the x term.
How Do You Find Gradient of a Line From Two Given Points?
The gradient of a line from the two given points, is equal to the ratio of the change of the y coordinates, to the change of the x coordinates. For any two points \((x_1, y_1)\), \((x_2, y_2)\), the gradient of the line is \(m = \dfrac{y_2  y_1}{x_2  x_1}\).
What Is The Formula For Gradient of a Line?
The formula to find the gradient of a line is \(m = \dfrac{y_2  y_1}{x_2  x_1} = Tanθ\).
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