Consider the pricing formula [P_{x}=frac{1}{R}left{bar{x}-beta_{x, M}left(bar{M}-P_{M} R ight) ight}] Let $N=a M+b$ for constants $a>0$ and $b$.

Consider the pricing formula

\[P_{x}=\frac{1}{R}\left\{\bar{x}-\beta_{x, M}\left(\bar{M}-P_{M} R\right)\right\}\]

Let $N=a M+b$ for constants $a>0$ and $b$. Show that substitution of $N$ for $M$ yields the exact same formula but with $N$ replacing $M$.