# Slope Formula Explicated With Examples

What is a slope? How is it calculated? Want to know what is the slope formula? Here, let's figure out through this post.

Narayani Karthik

Last Updated: Feb 20, 2019

Point Slope Formula

A straight line is a one which joins two distinct points. For instance, take the example of the staircase of your home. It is the simplest and best example of Math in everyday life. It is a slope and if you view it geometrically or on graph, you can make out the axes clearly.

_{2}- y

_{1}. Similarly, the x coordinate axes value would be x

_{2}- x

_{1}.

So, the formula of slope between two points can be calculated as:

m = (y

_{2}- y

_{1}) / (x

_{2}- x

_{1})

where m is the gradient of the image.

m = (y

_{2}- y

_{1}) / (x

_{2}- x

_{1}) = ∆y/∆x (rise/run),

where ∆ is the change indicated in the altitude and the horizontal distance.

So, the standard point slope equation is:

(y

_{2}- y

_{1}) = m (x

_{2}- x

_{1})

m = tan θ = Sin θ/Cos θ,

Example 1

A slope of 2 is given and the point for slope is (4,3) (x,y format). Calculate the equation in point slope form using the formula.

We know, the slope m = (y

=> (y

=> y - 3 = 2 (x - 4)

*Solution*:We know, the slope m = (y

_{2}- y_{1}) / (x_{2}- x_{1}) = ∆y/∆x=> (y

_{2}- 3) = 2 (x_{2}- 4)=> y - 3 = 2 (x - 4)

Example 2

A slope is formed by an angle of 30º. What is the gradient?

m = tan θ = tan 30º = 0.5773 (using a scientific calculator)

*Solution*:m = tan θ = tan 30º = 0.5773 (using a scientific calculator)