1. **State the problem:** We are given a circle with center $(-6, 1)$ and radius $1$. We need to write the equation of the circle in standard form and graph it. 2. **Formula for the equation of a circle:** The standard form of a circle's equation with center $(h, k)$ and radius $r$ is: $$ (x - h)^2 + (y - k)^2 = r^2 $$ 3. **Substitute the given values:** Here, $h = -6$, $k = 1$, and $r = 1$. Substitute these into the formula: $$ (x - (-6))^2 + (y - 1)^2 = 1^2 $$ 4. **Simplify the equation:** $$ (x + 6)^2 + (y - 1)^2 = 1 $$ 5. **Interpretation:** This equation represents all points $(x, y)$ that are exactly $1$ unit away from the center $(-6, 1)$. 6. **Graph description:** The graph is a circle centered at $(-6, 1)$ with radius $1$. It includes points one unit away in all directions from the center. **Final answer:** $$ (x + 6)^2 + (y - 1)^2 = 1 $$