How do you find the rate of change?

change in y over the change in x

we can find through gradient in graph or by calculation of numbers

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.

The rate of change can be defined by the following formula

rate of change = (change in quantity 1) / (change in quantity 2).

An example is the distance travelled by a car in a certain amount of time.

Rate of change is how quickly a measured quantity (e.g. speed) changes in time. To calculate this you need the change in the quantity (e.g. change in speed = final speed - initial speed) and then you need to divide that result by the change in time i.e. the time over which the measured quantity has changed.

E.g. to calculate the acceleration (rate of change of speed) of a car going from 5m/s to 10m/s in 20s you would do:

Acceleration = (10-5)/20 = 0.25m/s^2

How do find the rate of change

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

The rate of change in measured the change in Y over the change in X

You would have to differentiate

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

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

Rate of change is uesd to compare and deduce the mensurable change in the value of one quantity with respect to change in another quantity. It is possible to calculate rate of change in terms of increase or decrease in value of an amount or quantity. In physics, it is possible to calculate average velocity which is the rate of change of velocity,

Where Average velocity = ∆d/∆t

Also acceleration a =∆V/∆t

Examples of rates of change are speed (how far you travel over time) and acceleration (how your speed changes over time).

The maths for this is taken from the words.

For example if you travel 150 miles in 2 hours - you divide 150 by 2 - this gives you 75.

The units are miles per hour.

Answer is therefore 75 miles per hour (mph)

Work backwards to check.

If I travel for 2 hours at 75 mph. How far do I travel?

So I travel 75 miles in the first hour and 75 in the second hour .

The total travelled in 2 hours is 75 + 75 miles (or 75 x2).

Giving the answer 150 miles.

The rate of change is looking for the amount something would change per unit of time (seconds usually)

This can often be found by dividing what you are changing by how long it takes to change (dividing by the time)

If I had a bath tub with a hole in it with water falling out we could find the rate of change of the amount water in the bath tub

If the bath tub started with 100 litres and lost 30 litres in 1 minute

We could do 30 litres divided by 60 seconds giving a rate of change of 0.5 litres per second

I hope this helps!

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).