I'm not sure exactly what you're asking about, but perhaps this will help...
The equation \$V_A = V_B B + V_C C\$ is the same as this network:
Of course, you can decide to put the minus sign on C rather than B if you also switch the inputs to the summing node.
You have:
$$
\begin{align}
V &= \frac{ V_{\text{IN}} R_F + V_{\text{OUT}} R_A } { R_F + R_A } \\
&= V_{\text{IN}} \frac{R_F}{R_F+R_A} + V_{\text{OUT}} \frac{R_A}{R_F+R_A} \\
\end{align}
$$
So set:
$$
\begin{alignat*}{2}
V_B &= V_{\text{IN}}, &B = \frac{R_F}{R_F+R_A} \\
V_C &= V_{\text{OUT}}, &C = \frac{R_A}{R_F+R_A} \\
\end{alignat*}
$$
and apply the diagram.