How do you find the rate of change?

11 months ago


119 Replies




Vickie Shanahan

Need help with your studies? Find a qualified and experienced tutor on Sherpa.

Find a Tutor

119 Answers

Ekhveer Virk

Good depending at what level you teach

Tayyub Aslam

The change of 'y' divided by the change of 'x'


Use differentiation

For example, if we let a curve have a function y=f(x), and we know two points in the curve such as point P with coordinates (x,f(x)), and point Q with coordinates (x+h,F(x+h)), we workout the gradient of the curve by doing the change in Y coordinates divided by the change in X coordinates. After substituting the values into the formula for the gradient and simplifying, you will get the formula for differentiation from first principles !!!

syedahejab shah

from the graph, you will work out the change in the y-axis and divide this by the change in the x-axis.

Adeola Adedigba

You were not so specific about the exact rate of change you are hoping to find.

However, This should be a guide for you.

Rate of change =Change in output / Change in input

= Δ𝑦 / Δ𝑥

=(𝑦2−𝑦1) / (𝑥2−𝑥1)

=(𝑓(𝑥2)−𝑓(𝑥1)) / (𝑥2−𝑥1)

Damodharan Ranga Swamy

In math, you calculate the rate of change by using the coordinate points in a 2-d plane. The most practical way of understanding the rate of change is by studying & understanding velocity. Velocity can be defined as the rate of change in position. The rate of change in velocity gives us acceleration.

I hope this made sense.

Omar Choudhry

Rate of change = (Change in quantity 1) / (Change in quantity 2)

Alexander Burns

Rate of change = (Change in quantity 1)/ (Change in quantity 2)


If you are talking about the gradient then take the difference in y and divide it by the difference in x

Jason Kwok Profile Picture

Verified Sherpa Tutor

The rate of change is the ratio of the absolute change of quantity 1 to the absolute change of quantity 2:


Motivated teacher for Maths, English, Economics, German and Chinese!

Interested in booking a 1-1 lesson with me?

Click here to view my profile and send me a message.
Adrian Vecina Tercero

You can imagine the rate of change as how much something is changing in respect to something else. So if we have some value Y that is changing with respect to X we can work out the rate of change by dividing the change in Y by the change in X.

For example, if Y goes from 3 to 5, while X goes from 6 to 10, we know that the rate of change is (5-3) / (10-6) = 2 / 4 = 0.5. So in this case, the rate of change is a half (1/2).

Isra Ehbal

The rate of charge is great for the lessons

Svm tujtuj

To find out the rate at which a value has changed we find the difference between the 2 values first. We then find the difference as a percentage of the original value this is done by dividing the difference by the original value and then multiplying it by 100. This can be demonstrated by: ((New Value -Original Value) / Original Value) x 100.

Pia Profile Picture

Verified Sherpa Tutor

find the change in y over change in x using triangle on give graph

Science & Maths tutor - Alevel/GCSE & KS3 Struggling / Higher Atainers

Interested in booking a 1-1 lesson with me?

Click here to view my profile and send me a message.
Simranjeet Nagi

By differentiating the function, then inputting a value to find the rate of change at said value

More Maths GCSE Questions
Sherpa Badge

Need a Maths tutor?

Get started with a free online introductions with an experienced and qualified online tutor on Sherpa.

Find a Tutor