1. **State the problem:** We are given the function $f(x) = -\frac{1}{5}x$ and asked to graph it, then reflect the graph across the y-axis and write the function $g(x)$ describing the new graph. 2. **Recall the reflection rule:** Reflecting a graph across the y-axis changes every $x$ to $-x$. So, if $f(x)$ is the original function, the reflected function $g(x)$ is given by: $$g(x) = f(-x)$$ 3. **Apply the reflection:** Given $f(x) = -\frac{1}{5}x$, substitute $-x$ for $x$: $$g(x) = f(-x) = -\frac{1}{5}(-x)$$ 4. **Simplify the expression:** $$g(x) = -\frac{1}{5} \times (-x) = \frac{1}{5}x$$ 5. **Interpretation:** The reflection across the y-axis changes the slope from $-\frac{1}{5}$ to $\frac{1}{5}$. The graph of $g(x)$ is a line with positive slope $\frac{1}{5}$. **Final answer:** $$g(x) = \frac{1}{5}x$$