1. The problem asks for the geometric interpretation of the partial derivative $f_x(a,b)$ of a function $f(x,y)$ at the point $(a,b)$. 2. Recall that the partial derivative $f_x(a,b)$ measures the rate of change of the function $f$ with respect to $x$ while keeping $y$ fixed at $b$. 3. Geometrically, the surface is given by $z = f(x,y)$. Fixing $y=b$ gives a curve on the surface defined by $z = f(x,b)$. 4. The partial derivative $f_x(a,b)$ is the slope of the tangent line to this curve at the point $(a,b,f(a,b))$. This tangent line lies in the plane $y=b$. 5. Therefore, the correct interpretation is: **B. The slope of the tangent line to the curve formed by the intersection of the surface $z = f(x,y)$ and the plane $y = b$.**