Slope Formula
Before learning the slope formula, let us recall what is the slope. The slope 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 slope formula is used to calculate the inclination or steepness of a line. The slope formula calculates the slope of any line by finding the ratio of the change in the yaxis to the change in the xaxis.
What Is the Slope Formula?
The x and y coordinates of the line are used to calculate the slope of the line. The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as
m = Δy/Δx
where
 m is the slope.
 Δy is the change in ycoordinates.
 Δx is the change in the xcoordinates.
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. So
tan θ = Δy/Δx
From the graph, we observe:
Δy = y_{2 }− y_{1}
Δx = x_{2 }− x_{1}
Thus, the slope formula is given as:
Slope = m = tan θ = (y_{2 }− y_{1})/(x_{2 }− x_{1})
Let us see the applications of the slope formula in the following solved examples.

Example 1: Using slope formula, calculate the slope of the line 2y = 8x + 9.
Solution:
To find: Slope of a line
Given: Equation of line is 2y = 8x + 9
Using slope formula,
y = mx + b
Hence, we try to bring the equation to this form. We make the coefficient of y = 1,
y = 4x + 4.5
Clearly, the coefficient of x is found to be 4. Hence, our slope will be the same as the coefficient of x.
Answer: Slope of the given line = 4

Example 2: Using slope formula, calculate the slope of the line x = 5.
Solution:
To find: Slope of a line
Given: Equation of line is x = 5
Using slope formula,
y = mx + b
Rewriting the given equation in the general form:
(0)y = x − 5
Now, we try to make the coefficient of y as 1. In order to do so, we will have to divide both sides by Zero.
We know that mathematically, if any real is divided by Zero, then the value can not be determined.
In this case, the coefficient of x divided by Zero will give us our slope. But we know that the answer will not be defined in such a case.
So we can safely say that our slope is not defined in such cases.
Answer: Slope is not defined for the given case.