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).

The rate of change tells us how one thing changes compared to another. For example, if you're looking at how far a car travels over time, the rate of change would be its speed—how many meters the car moves every second.

First we need to know how much each of these things changes. You do this by subtracting the starting value from the ending value. For example, if a car moves from 10 meters to 30 meters in 4 seconds, the change in distance is 20 meters, and the change in time is 4 seconds.

Then you divide the change in distance by the change in time to get the rate of change. In this case, the car is moving at 5 meters per second. This means every second, the car travels 5 meters.

Hope this helps :)

The rate of change measures how one quantity changes relative to another. In mathematics, it is often calculated using derivatives in calculus or the difference between two points in algebra. Here are the common methods to find the rate of change:

1. Average Rate of Change (Algebraic Approach)

The average rate of change between two points on a function is calculated as the slope of the line connecting the points. This is given by:

2. Instantaneous Rate of Change (Using Derivatives)

The instantaneous rate of change of a function at a specific point is the value of the derivative at that point.

This gives the slope of the tangent line to the curve at x=ax = ax=a, representing how the function changes at that exact point.

The rate of change is the amount of change per unit time. We can find the rate of change by dividing the change in our measurement by the time it took for that change to occur. For example, if our speed increased by 10 m/s over 5 seconds, our rate of change (acceleration) would be n10/5=2ms^-2

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)