Rates of Change


How do you find the rate of change?

1 year ago


126 Replies




Vickie Shanahan

126 Answers

Angie Muyeke

The rate of change can be found on a straight-line graph by selecting two coordinates and dividing the change in the y-values by the change in the x-values. This can be shown in the formula : m = y2-y1/ x2-x1 with m representing the gradient of the straight-line. Additionally, x and y can be two different variables and the formula is used to calculate average speed or average velocity.The rate of change of a straight line is equivalent to the gradient of a straight line graph. However, we use differentiation with non-linear graphs to find the rate of change at a particular point. This is another topic in itself.

Milton Tom

Frays of change is how much x. Ganges w time or another variable . So this can be done by working out the gradient of a graph or differentiating If it is an expression

Ajit Kumar

Rate of Change is a general concept and it is applied in various subjects like Maths and Science. Let's understand it by taking an example.

In Time T, I reached from D1 to D2. What is the Rate of change.

So for this, Let's calculate

the Change in Distance= D2-D1

time taken = T

So, Rate of Change = (D2-D1)/ T

i.e change in distance per unit time. This is Rate of change.

Unai Llona Carbajo

Derivatives are the best tool, but not for everyone... Considering two variables (distance and time, for example), you can also take the first and last value of both in a certain process, subtract the ones from the same variable (e.g. last and first distances of the bus from your position) and divide the subtractions of different variables. By doing this with position/distance and time, the rate of change you get is the speed of the object you're analyzing!

Amber Cummins

There are a couple of ways to find this. If your data is displayed in graph format, you can find the rate of change by dividing the change in y-values by the change in x-values. If you are talking about the instantaneous rate of change (this is called the derivative of a function) then we need to look further at the function itself.

Lewis Lovell

Hello Mrs Vickie Shanahan. There isn't much context to your question here, so I'll keep my response as general as possible:

The rate of change describes a relationship between a dependent and an independent variable. For example, the rate of change of velocity with time or the rate of change of temperature with distance.

In a simple mathematical case, we'd write this as the change in the dependent variable (temperature, dT) over a fixed interval of the independent variable (distance, dx)

Which is mathematically written as dT/dx, or as shown in the graph, dy/dx.

It is then clear that for the linear relationship in the above graph, the rate of change is dy/dx = (y1-y2)/(x2-x1) = (6-3)/(8-4).

Bilal Chaudhry

Rate of change= gradient

In a linear equation, gradient= y1 – y2 / x1 x2

In a quadratic equation, gradient = dy/dx.

Faizan Ahmed

For a linear set of values the rate of change will be the change in y-values divided by the change in x-values in other words the gradient of a straight line. In the set of values relating to a curved line the rate of change on each point can be found by differentiating the equation of that curve and using the values of x of the point you need to find the rate of change at.


How do find the rate of change

Archita Sinha

The rate of change on a line graph is called the gradient and is calculated by the change in y axis/ change in x axis. What this means is that you find 2 points on the line and find the difference between the y coordinates and divide that by the difference in x axis.

George Asquith

The rate of change is how much one quantity changes per unit of another amount. Normally this is how much y changes for every set amount that x increases or decreases. This is the same as the gradient (in straight lines gradient is fixed and is shown as m in y=mx+c, in other graphs, the gradient changes). This can be calculated by having two points each with x and y coordinates. y1-y2 divded by x1-x2.


The rate of change = change in y over change in x , if you are given 2 coordinates e.g (2,0) (3,3) and you want to find the rate of change. You would simply do 3-0 / 3-1 which would give you 3/2. This will give you a gradient y=3/2x + c. To find c you would simply sub one of the coordinates back in to this equation.


The change in the y axis divided by the change in the x-axis

Stephen Angelo Savvanis Nasiotis

Hi Vickie, Rate of Change is defined as the change in some quantity over unit time. For example rate of change of Distance would be speed measured in km/h. Often in a Maths GCSE paper this would involve a question with a graph, for example having Distance on the y-axis and Time on the x-axis. The rate of change would be the gradient of the line on the graph.

Babatunde Omonojo

This depends on what you mean by the rate of change. In simple terms, the rate of change can be found by finding the change in y and then dividing it by the change in x. For example, if a car travels 60km in 3 hours, the distance (km) traveled will be the y-axis, and time (hours) will be the x-axis. The change in y will be 60km and the change in x will be 3 hours. The rate of change will be 60/3 = 20km/hr

Think you can help?

More Maths GCSE Questions
Sherpa Badge

Need a GCSE Maths tutor?

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

Find a GCSE Maths Tutor