1. **State the problem:** We need to reflect the point $(-3,1)$ across the y-axis. 2. **Formula for reflection across the y-axis:** When a point $(x,y)$ is reflected across the y-axis, its x-coordinate changes sign, while the y-coordinate remains the same. The formula is: $$ (x,y) \to (-x,y) $$ 3. **Apply the formula:** For the point $(-3,1)$, $$ (-3,1) \to (-(-3),1) = (3,1) $$ 4. **Explanation:** Reflecting across the y-axis means flipping the point horizontally. Since the original x-coordinate is $-3$, its reflection is $3$. The y-coordinate stays $1$ because reflection across the y-axis does not affect vertical position. 5. **Final answer:** The reflected point is **$(3,1)$**.