From $p(x)=\frac{4}{5}B(x)-5$, add 5 to both sides and then multiply by the reciprocal of $\frac{4}{5}$.

After you get $B(x)$ in terms of $p(x)$, substitute your expression for $p(x)$ and combine constants using a common denominator.

In Desmos, enter points $A=(10,51)$ and $B=(22,35)$.

Compute $m=\frac{y(B)-y(A)}{x(B)-x(A)}$ and $b=y(A)-m\cdot x(A)$, then enter $p(x)=mx+b$.

Enter $B(x)=\frac{5}{4}(p(x)+5)$ and simplify the expression Desmos shows.

Compare the simplified form of $B(x)$ to the four options and select the exact match.

The points on the line $p(x)$ are $(10,51)$ and $(22,35)$.

Slope:

Use $(10,51)$ to find $b$ in $p(x)=mx+b$:

So

Given

add 5 to both sides and multiply by $\frac{5}{4}$:

Substitute $p(x)=-\frac{4}{3}x+\frac{193}{3}$:

Therefore, $B(x)=-\frac{5}{3}x+\frac{260}{3}$.