Rates of Change


How do you find the rate of change?

1 year ago


167 Replies




Vickie Shanahan

167 Answers


To find the rate of change, you must divide the change in y by the change in x (if using a graph, where y is the vertical axis and x is the horizontal axis).

Leon Cragg

the change in y-values by the change in x-values.

Sonya Pervez

The rate of change (ROC) is how much the value of something changes over a period of time and it is given in percentage terms.

To find this you first calculate the change in "Y" values (or the change in an outcome variable) divided by the change in "X" values (or the change in input variables).

So if my tutoring time increases from 3 hours in week 1 to 16 hours in week 2 and my income increases from £45 per week to £240 per week, Y values are my income and X values are the work hours I put in. r

To calculate the ROC I would do the following.

(240 - 45) / (16 - 3) = 195 / 13 = 15% rate of change in my earnings between week 1 and week 2.

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If you take the change in Y values and divide that with the change in X-values the result will be a rate of change,

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In a graph of a value vs time, it would be the gradient. Otherwise simply divide the difference in any particular value by the time taken.

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The rate of change can be found by calculating the difference in the values of a quantity over a certain period of time or another variable. It is often calculated using the formula:

Rate of change = (Change in quantity) / (Change in time or another variable)

For example, to find the rate of change of distance with respect to time, you would divide the change in distance by the change in time. This gives you the speed or velocity.

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Timothy M Lewis

Assuming rate of charge is the rate of flow of charge, this is known as current (I). This can be found by dividing charge (Q) by time (t) - I = Q/t

Darcy Peake

The rate of change refers to how much something for example distance is changing in a specific unit of time. In order to work out the rate of change, you must divide the thing that is changing with how much it has changed in such a unit of time.

Hammad Shahid

The rate of change measures how a quantity changes over time or across space. It's often represented as the slope of a line connecting two points on a graph.


Rate of change can be calculated by the amount of a specific quantity is changing by the time it took for the change to hapen. A common example in physics in speed which is simply rate of change of position(or distance). If a car changes its position by 20 miles in 30 minnutes then its average speed(or rate of change of position) is 20miles divided by 30min(or 0.5 hr) which is 40 miles per hr

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Difference divided by the time.

In terms of a graph, this will be the change in the y-axis divided by the change in the x-axis (aka slope).

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Olivia Hodnett

By finding the gradient of the line. You can do this by using the formula: m = (y2 — y1) / (x2 — x1). Where m is the gradient.

Stavros Savva

Divide the change of one variable with the change of the other variable

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).

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!

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