Final answer:
The values of A, B, and C for the equation Ax + By = C that represents a horizontal line through the point (9, 3) would be A = 0, B = 1, and C = 3, indicating the equation y = 3.
Step-by-step explanation:
To determine the values of A, B, and C for the equation Ax + By = C that represents a horizontal line through the point (9, 3), we need to recognize that the slope of a horizontal line is zero. This means that there is no change in y for any change in x, so the x term in the equation will not be present since its coefficient would be zero (A = 0).
The general equation of a line can be given as Ax + By = C, but for a horizontal line, it simplifies to y = C, because Ax or the change in x must be zero. Given that the line passes through the point (9, 3), we know that when x is 9, y must be 3. Substituting these values into the equation y = C gives us 3 = C. Therefore, C = 3.
In conclusion, for a horizontal line through the point (9, 3), the equation is y = 3, which means A = 0, B = 1 (since any number times 1 is itself, and B is with y), and C = 3.