Rates of Change


How do you find the rate of change?

1 year ago


168 Replies




Vickie Shanahan

168 Answers

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

Yunho Kwon

Linear functions have a constant rate of change which is represented as the gradient of the graph.

It is simply the change of y-values with respect to x-values i.e. (y1-y2) / (x1-x2) where (x1,y1), (x2,y2) are the coordinates

Leon Cragg

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

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.

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The Rate of change (ROC) is the increase or decrease of one value related to another value.

The speed of a car for instance is the distance covered divided by the time taken.

In mathematics this can be the gradient of a graph in general terms.

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Junaid Khalid

The average rate of change represents the average rate at which something changes from one point to another.

So you need to set up the equation like this:

Rate of change of {x} = (change in x) divided by time taken for the change to happen.

E.g. Rate of change of distance is acceleration.

a = d2 - d1 / t

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

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Sam Morris

To find the average rate of change of a function over an interval, you can use the formula:

Average Rate of Change = (Change in Y) / (Change in X) = (ΔY) / (ΔX)

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You would have to differentiate

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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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Paul Hunt

This is easier to work out from a graph, the rate of change is the gradient of the line - the change in y divided by the change in x. However, you might not have time in exam conditions to draw a graph when it's not asked of you, so I would suggest picking two points of the data - ignoring outliers if there are any. Calculate the difference between them by taking them away from each other, then divide that by the difference in time between them. This will give you the rate of change.


The rate of change (ROC) is the speed at which a variable changes over a specific period of time


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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