Gradient Formula
Before going to learn the gradient formula, let us recall what is a gradient. The gradient is also known as a slope. The gradient of any straight line depicts or shows that how steep any straight line is. If any line is steeper then the gradient is said to be larger. The gradient of any line is defined or represented by the ratio of vertical change to horizontal change. In terms of a triangular figure, the ratio of the length of the vertical side of a triangle to the length of the horizontal side of a triangle determines the gradient. In basic terminologies, the gradient formula tells us the degree by which any road or any line goes up or down. The gradient formula is explained below with solved examples at the end.
What Is Gradient Formula?
Since we have seen that gradient is nothing but slope, we use the slope formula to find the gradient as well. Gradient formula can be expressed as,
m = (rise/run)=(y_{2}y_{1})/(x_{2}x_{1} )
Where,
 (x_{1},y_{1}) = coordinates of the first point
 (x_{2},y_{2}) = coordinates of the second point
Let us learn the gradient formula along with a few solved examples.
Solved Examples Using Gradient Formula

Example 1: Find the gradient of the line joining two points (3,4) and (5,6).
Solution
To find: To find: Gradient of a line
Given: (x_{1},y_{1}) = (3,4)
(x_{2},y_{2}) = (5,6)Using gradient formula,
m = (rise/run) = (y_{2}y_{1})/(x_{2}x_{1})
m= (64)/(53)
m = 2/2
m = 1
Answer: The gradient of the line joining two points is 1

Example 2: Find the gradient of the line joining two points (3,2) and (7,5).
Solution
To find: Gradient of a line
Given: (x_{1},y_{1}) = (3,2)
(x_{2},y_{2}) = (7,5)Using gradient formula,
m = (rise/run) = (y_{2}y_{1})/(x_{2}x_{1} )
m = (5(2)) / (73)
m = 7/4
m = 1.75
Answer: The gradient of the line joining two points is 1.75.
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