Let $f: M \rightarrow N $ be a smooth map with $M,N$ smooth compact oriented manifolds, without boundary and with the same dimension $n$ with $N$ connected show that $$deg(f)=I(graph(f), M \times \{y\})$$ for any $y \in N$
First i know that $deg(f)= \sum_{f(x)=y} sign(df_x)$ and $I(graph(f), M \times \{y\})$ is the sum of the oriented numbers of the elements in $graph(f) \cap (M \times \{y\})$ the given $x \in graph(f) \cap (M \times \{y\})$ i try to see that the oriented number of $x$ is precisely $sign(df_x)$ but i not sure howw see these
Any hint or help i will be very grateful.