# hey if dy/dx= -2 why is it wrong to say that y is alwats decreasing at a rate of -2? I don't really get it.

It is better to say that y is always decreasing with a slope of -2 on a graph of y(x), or at a rate of -2 per change in x. Saying that a rate is a number does not say enough about what variables are involved.

## To understand why it is incorrect to say that y is always decreasing at a rate of -2, let's break down the meaning of the derivative dy/dx = -2:

The derivative dy/dx represents the rate of change of y with respect to x, or the instantaneous slope of the graph of y(x) at any given point. In this case, we are given that dy/dx = -2.

When the derivative dy/dx = -2, it means that for every unit increase in x, y decreases by a rate of 2 units. However, it does not mean that y always decreases at a rate of -2.

To see why, consider a simple example where y = x^2. The derivative of y with respect to x is given by dy/dx = 2x. If we evaluate this derivative at x = 1, we get dy/dx = 2(1) = 2. This means that at x = 1, the slope of the graph of y(x) is 2.

Now, if we evaluate the derivative at x = -1, we get dy/dx = 2(-1) = -2. Here, the slope of the graph of y(x) is -2. However, notice that the value of dy/dx changes depending on the value of x. This means that the rate at which y changes depends on the value of x and is not a constant -2.

Therefore, saying that y is always decreasing at a rate of -2 is incorrect and misleading. The derivative dy/dx = -2 only tells us the instantaneous rate of change at any given point on the graph, but it does not imply a constant rate of change for all values of x.