Final answer:
The total number of lattice points on the graph is 1.
Step-by-step explanation:
The equation of the graph is x^2 + y^2 + 11x - 13y + 73 = 0. To find the total number of lattice points on the graph, we need to find the integral solutions for x and y that satisfy the equation.
We can rearrange the equation to get: (x + 5.5)^2 - 5.5^2 + (y - 6.5)^2 - 6.5^2 = -11.25.
Since the sum of two squares is a negative number, the only integral solution for x and y is (x, y) = (0, 0).
Therefore, the total number of lattice points on the graph is 1.