Rates of Change
How do you...
1 year ago
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!
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.
The rate of change is how something is changing. Imagine you have a toy car that moves on a track. The rate of change tells you how fast the car is moving or if it's going faster or slower.
To find the rate of change, you can look at two things: how much something changes and how much time it takes. For example, if the car moves 10 centimeters in 2 seconds, the rate of change is 5 centimeters per second because it moves 5 centimeters each second.
You can also think of the rate of change as a slope on a hill. If the hill is steep, it means things are changing quickly. If it's not very steep, things are changing slowly.
So, the rate of change is like a measurement that tells you how fast something is changing or how steep the change is. It can help you understand how things are moving or growing.
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.
we can find through gradient in graph or by calculation of numbers
distance travelled divided by the time
The rate of change = change in y over change in x , if you are given 2 coordinates e.g (2,0) (3,3) and you want to find the rate of change. You would simply do 3-0 / 3-1 which would give you 3/2. This will give you a gradient y=3/2x + c. To find c you would simply sub one of the coordinates back in to this equation.
The rate of change is also known as the gradient or slope.
Rate of change = (change in quantity 1) / (change in quantity 2)
Given 2 points (x1, y1) and (x2, y2), the rate of change between them is:
Δy / Δx = (y2 - y1) / (x2 - x1)
The change in the y axis divided by the change in the x-axis
change in y-values divided by change in x-values
Rate of change = change in y/ change in x
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