Final answer:
The correct standard form of the equation for the graphed line with a slope of 3 and a y-intercept of 9 is 3x - y = -9. This maintains the convention of having a non-negative A in the standard form Ax + By = C.
Step-by-step explanation:
The question revolves around the standard form of the equation of a line. The standard form is generally expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative. Given the slope (m) is 3, and the y-intercept (b) is 9, the slope-intercept form of the line is y = 3x + 9.
This can be transformed to standard form by subtracting 3x from both sides to yield -3x + y = 9, which can be multiplied by -1 to maintain A as a non-negative number: 3x - y = -9. Thus, the true options about the standard form are that the value of A can be -1 if B is 0 and C is 3, or the related equation 3x = -9, which is derived from the standard form by setting y to zero.
Therefore, the correct standard form of the equation for the graphed line is 3x - y = -9. This reflects the given slope and y-intercept and maintains the convention of A being non-negative in standard form equations.