Final answer:
The graph shown on the xy plane displays both a line and a parabola, thus the correct option is 3.
Step-by-step explanation:
The graph shown on the xy plane displays both a line and a parabola. The line extends along the first and fourth quadrants and passes through the points (3, 3), (6, 0), (8, -2), and (10, -4). This line can be represented by the equation y = -x + 6, where -x represents the slope and 6 represents the y-intercept. The closed dot at the point (3, 3) indicates that this point is included in the line, which means that the point satisfies the equation.
The parabola extends along the first and second quadrants and passes through the points (3, 15), (2, 10), (10, -2), and (-4, 20). The vertex of the parabola lies at (0, 6). This parabola can be represented by the equation y = -x^2 + 6x + 6, where -x^2 represents the squared term, 6x represents the linear term, and 6 represents the constant term. The open dot at the point (3, 15) indicates that this point is not included in the parabola, which means that the point does not satisfy the equation.
The line and the parabola intersect at the point (10, -2), which means that this point satisfies both the line equation and the parabola equation. This point is the solution to the system of equations y = -x + 6 and y = -x^2 + 6x + 6, and it can be found by solving for x and y using any method of solving systems of equations. The fact that the line and the parabola intersect at a single point confirms that both the line and the parabola are graphed on the xy plane.
In conclusion, the graph displays both a line and a parabola, and the intersection point (10, -2) satisfies both equations. This confirms that option 3, both line and parabola, is the correct answer.