Final answer:
The question pertains to mathematical concepts including graph theory, vectors, spatial reasoning puzzles, and the graphing of a linear equation. The illustrations and algebraic functions provided are essential for understanding different aspects of high school-level mathematics.
Step-by-step explanation:
The question seems to describe a mathematical concept which may be related to graph theory, where you are asked to illustrate a model with specific properties; however, it also contains elements that pertain to geometry and algebra. Considering the diverse elements, let's focus on the mathematical illustrations provided.
To draw a vector representing 9 blocks to the east, you would use a ruler and protractor for precision. When studying spatial reasoning puzzles, connecting nine dots with four straight lines without lifting your pencil is another challenge.
Regarding the linear equation y = 9 + 3x, you are looking at an algebraic function where 'b' which typically represents the y-intercept is 9, and 'm' which represents the slope is 3. To graph this function, you create a table with values of 'x' and calculate the corresponding 'y' values. Plotting these points on the Cartesian plane, a line is drawn through the points to represent the equation visually.