(4) If the line $y=x-3$ is tangent to the curve $y=\mathrm{e}^{x+a}$, then the value of the real number $a$ is ( ).
(A) -4
(B) -2
(C) 2
(D) 4
(4) A Hint: Let the x-coordinate of the tangent point be $x_{0}$. At $x=x_{0}$, the slope of the curve $y=\mathrm{e}^{x+a}$ is $\mathrm{e}^{x_{0}+a}$. The slope of the line $y=x-3$ is 1. Therefore, $\mathrm{e}^{x_{0}+a}=1$, which gives $x_{0}=$ $-a$. Thus, the y-coordinate of the tangent point $\mathrm{e}^{x_{0}+a}=1=x_{0}-3$, i.e., $1=-a-3$, so $a=$ -4.