# How do you rate of change

Or we could say, 4 meters per second. So let me do this in a more fun color. Or one of the ways to think about a line or a linear function is that the rate of change of one variable with respect to the other one, is constant.

But there are two other kinds of lines, horizontal and vertical. What is the slope of a flat line or level ground? Of a sheer wall or a vertical line? No matter which two points we choose on the line, they will always have the same y-coordinate.

## Rate of Change Formula

That means the rise, the vertical difference between two points, will always be zero. What happens when we put a rise of 0 into the slope formula? Zero divided by any number is zero. The slope of a horizontal line is always 0. How about vertical lines? In their case, no matter which two points we choose, they will always have the same x-coordinate. That means that the run, the horizontal difference between two points, will always be zero. When we put a run of 0 into the slope formula, the equation becomes.

All vertical lines have a slope that is undefined. As you can see, slopes play an important role in our everyday life. You may walk up a slope to get to the bus stop or ski down the slope of a mountain. The slope formula, writtenis a useful tool you can use to calculate the vertical and horizontal change of a variety of slopes. B Rise minus run C The sideways movement over the up or down movement along a line or surface. We could say the average rate of change from when we go from t equals 0 to t equals 3 That's going to be the slope of this secant line So let me draw that.

So let me do this in a more fun color.

Slope and rate of changeI'll do it in this color All right So as I said the actual Instantaneous rate of change is constantly changing. In this case it's increasing, and we'll need calculus for that. But now we could think about average rate of change which would be the slope of the line that connects these two points.

And once again, it's only an average rate of change. As we see, the actual curve its rate of change is lower earlier on, and then it's rate of change is higher as we get closer and closer to 3 seconds.

But the average rate of change is going to be the slope of this line right over here.

And we could think about that. This is going to be our change. So the slope of this line, is going to be a change in distance over change in time. An average rate of change especially when you're talking about a curve like this it depends on what starting and ending point This is the average rate of change for the first 3 seconds, is going to be- Well what is our distance right at the third second?

Well, it's going to be d of 3. Now what was our initial distance?

It's going to be d of zero. So this expression right over here. It's going to give me my change in distance.

#### How Do You Find the Rate of Change Between Two Points in a Table?

It's going to give me my change in distance right over here Let me rate. It actually maybe I could do it this way So I could do it over here. So our change in distance is this. Change in distance which is d of 3, d of 2 minus d of zero. So it gives us this height and then we want to divide it by our change in time Well, we finished it 3 seconds, and we started at zero seconds.

And notice, all this is, is change in your you axis over change in your horizontal axis So it is change the slope of this line right over here. So what is this going to be?

Well, d of 3 after 3 seconds. We had a distance of 1 meter, so our change in distance how It's 9 meters, and you see that right over here. Change in distance is 9 meters We go from 1 meter to 10 meters and and we increase 9 meters So that's why it's a positive value. And our change in time?

So let's say that we can kind of view this as our endpoint right over here. So this is our end. This is our start. And we could have done it the other way around. We would get a consistent result. But since this is higher up on the list, let's call this the start. And the x is a lower value.

### How Do You Find the Rate of Change Between Two Points on a Graph?

We'll call that our start. This is our end. So we start at 6.

If coordinates of any two points of a line are given, then the rate of change is the ratio of the change in the y-coordinates to the change in the x-coordinates. The rate of change between the points x 1y 1 and x 2y 2 is given as. Over 11, live tutoring sessions served! To get the best deal on Tutoring, call Toll Free. Rate of Change Formula.

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