1. The problem is to create the silhouette of a dog on a coordinate plane with $x$ and $y$ values ranging from $-6$ to $6$. 2. To do this, we need to understand that a silhouette can be represented by a set of points or curves that outline the shape. 3. Since this is a 6th-grade level task, we can approximate the dog's shape using simple geometric shapes like circles, ellipses, and lines. 4. For example, the head can be a circle centered at $(0,2)$ with radius $1$, the body an ellipse centered at $(0,0)$ with horizontal radius $3$ and vertical radius $2$, and the tail a line segment from $(3,0)$ to $(5,1)$. 5. We can write the equations for these shapes: - Head: $$ (x-0)^2 + (y-2)^2 = 1^2 $$ - Body: $$ \frac{x^2}{3^2} + \frac{y^2}{2^2} = 1 $$ - Tail: line segment from $(3,0)$ to $(5,1)$ can be parameterized as $$ x = 3 + 2t, y = 0 + t $$ for $0 \leq t \leq 1$ 6. By plotting these shapes together on the coordinate plane, we get a simple silhouette of a dog. 7. This approach uses basic shapes and is suitable for 6th-grade understanding. Final answer: The silhouette is approximated by the circle $$ (x)^2 + (y-2)^2 = 1 $$, the ellipse $$ \frac{x^2}{9} + \frac{y^2}{4} = 1 $$, and the tail line segment from $(3,0)$ to $(5,1)$.