How do you find the rate of change?

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

Rate of change of what?

The rate of change of anything is usually given by its end value, minus its start value, divided by time

for example momentum=0 at t=0s, and momentum=5 at t=10s, rate of change = (5-0)/10 = 5/10 = 1/2

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

Find the change in y, and divide it by the change in x!

For example...

On a graph, we may find two points (5,4) and (6,8).

We can calculate rate of change by taking the x values (5 and 6), and finding the difference between them (6-5=1). We do the same for the y values (4 and 8), with the difference being 4.

Therefore, the rate of change = 4 / 1 = 4!

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.

Rate of change generally refers to how something changes with respect to something else. For example, velocity is the rate of change of distance with respect to time, and acceleration is the rate of change of velocity with respect to time.

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

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.

This is an easy thing to find out. If you have a straight line on a X-Y graph, the formula you would use is y=mx+c. The rate of change is m in this formula is is how steep the line is . To calculate m for this formula you choose two separate points on the line (taking note of their X-Y coordinates). Then you take the difference between the y coordinates then take the difference between the x coordinates. Then you take these two numbers and divide the difference between the y coordinates by the difference between the x coordinates. This will give you the steepness of the line which is m in the formula of a straight line.

Rate of Change = (Change in Output) / (Change in Input)

• Change in Output: This refers to the difference between the final and initial values of the quantity you're measuring (often denoted by y).
• Change in Input: This refers to the difference between the final and initial values of the independent variable (often denoted by x).

To find the rate of change of something you calculate how much the “something” has changed by and then divide it by the number of seconds that have passed.

Hi Vickie!

The rate of change of a system can be found in several different ways depending on the particulars of the question. For this answer, I will assume you're comfortable with single differentiation, and we will talk about some of the cases where there are several derivatives at play! If you would like help with single derivatives for rates of change, then please follow this reply up with another question :)

The crucial thing to ask ourselves is on what conditions (also known as "independent variables") does whatever we are measuring (our "dependent variable") depend on? Here is a quick scheme and example for the rate of change of a dependent variable which depends on two factors:

Let V be the volume of a cuboid with a square base with sides of length x meters, and a height of y meters. Then from geometry we know the volume is given by

V(x,y) = y*(x^2),

where we write V(x,y) because V depends on both x and y, and x^2 is typed notation for x squared. Now if we change x by a small amount, how does this affect V? This is of course a lengthier way of asking: what is the rate of change of V with respect to x? We can calculate this with a derivative, which measures precisely this! If we remember our differentiation, we get:

The rate of change of V with respect to x is given by:

dV/dx = 2xy.

The rate of change of V with respect to y is given by:

dV/dy = x^2.

Now, what if both x and y are changing at the same time? Then we need to consider a global rate of change (which we will label dV/dt), and this is where things get a bit tricky. In summary, we will add together both rates of change! However, we need to be careful to account for how fast x and y are both changing.

Let's pretend that x changes at a rate of 1meter per second, and y changes at a rate of 2meters per second. Then if we add the rates of change, we get:

dV/dt = x^2 + 2xy,

but this is not the whole story! As y is changing at double the speed than x, intuitively we should make sure that the term dV/dy has double the effect on the global rate of change. The correct answer is therefore:

dV/dt = x^2 + 4xy.

This example illustrates an intuitive approach to how rates of change work with several moving parts. The topic called implicit differentiation then takes these ideas and makes them much more automatic! In summary,

The global rate of change is found by multiplying the individual rate of change of each variable by how fast that variable is changing, and adding all these terms together for all independent variables.

Hope this helps!

Alberto

in general, finding the gradient of any function will give you the rate of change of it at a certain point. if you don't know calculus, then draw a tangent, pick two coordinates and then find the change in y divided by the change in x. if you do know calculus, differentiating the function once and then substituting in the x coordinate of the point of interest will give you the gradient at that point

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.

We can find the rate of change by calculating the gradient of the curve or line. We identify two points on the line. Next we find the difference in the y-axis points and divide by the difference in the x-axis points. E.g. (Y2 - Y1)/(X2 - X1)