AMC 12 2020a Problem 12

Line $\ell$ in the coordinate plane has the equation $3x - 5y + 40 = 0$. This line is rotated $45^{\circ}$ counterclockwise about the point $(20, 20)$ to obtain line $k$. What is the $x$-coordinate of the $x$-intercept of line $k?$

$\textbf{(A) } 10 \textbf{(B) } 15 \textbf{(C) } 20 \textbf{(D) } 25 \textbf{(E) } 30$