Final answer:
The values for a horizontal line equation Ax + By = C through the point (9, 3) are A = 0, B = 0, and C = 3, because a horizontal line has a slope of 0 and its equation is y = k, where k is the constant y-value for all points on the line.
Step-by-step explanation:
To find 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 understand the nature of a horizontal line in the coordinate system. A horizontal line has a slope (m) of 0, which means that the change in y is zero regardless of the change in x.
Therefore, the equation of a horizontal line is always in the form of y = k, where k is the y-coordinate of every point on the line. Since the line goes through the point (9, 3), the value of k is 3. So, the equation of the line is y = 3. This means that B must be 0 to ensure the line remains horizontal, and C is the y-value of the line, which is 3. Since the coefficient A accompanies the x variable and x can be any value without affecting y in a horizontal line, A should be 0. Therefore, the values that make the equation a horizontal line are A = 0, B = 0, and C = 3.