To determine the derivative of the function \( y = -2x - 1 \) at the point \( x = -1 \), we first need to find the derivative function.
The function \( y = -2x - 1 \) is a linear function. The derivative of a linear function \( y = mx + b \) is the slope \( m \). In this case, the slope \( m \) is \(-2\).
Thus, the derivative function is:
\[ \frac{dy}{dx} = -2 \]
Since the derivative is constant, the derivative at any point, including \( x = -1 \), is simply:
\[ \frac{dy}{dx} \bigg|_{x=-1} = -2 \]
So, the derivative of \( y \) at the point \( x = -1 \) is \(-2\).