2. The function expression of the image $l_{2}$, which is symmetric to the image $l_{1}$ of the linear function $y = a x + b$ with respect to the line $y = -x$, is $\qquad$ .
2. $y=\frac{1}{a} x+\frac{b}{a}$.

The line $y=a x+b$ intersects the $x$-axis and $y$-axis at points $A_{1}\left(-\frac{b}{a}, 0\right)$ and $B_{1}(0, b)$, respectively. The points $A_{1}$ and $B_{1}$, when reflected over the line $y=-x$, become $A_{2}\left(0, \frac{b}{a}\right)$ and $B_{2}(-b, 0)$. Using the method of undetermined coefficients or the relationship between slope and intercept, the line passing through points $A_{2}$ and $B_{2}$ is $y=\frac{1}{a} x+\frac{b}{a}$.

Therefore, the function expression of the image of the linear function $y=a x+b$ reflected over the line $y=-x$ is $y=\frac{1}{a} x+\frac{b}{a}$.