Final answer:
The equation of a line parallel to x=9 and passing through (0,2) is x=0, since x=9 represents a vertical line and parallel lines have the same orientation.
Step-by-step explanation:
To write an equation of a line that is parallel to the given line x=9 and passes through the point (0,2), we need to recognize that the equation x=9 represents a vertical line. Vertical lines have an undefined slope, and any line parallel to a vertical line must also be vertical. Therefore, the equation of the line we are looking for must also be a vertical line.
Since the line must pass through the point (0,2), the x-coordinate of every point on the line must be 0 to satisfy this condition. Hence, the equation of our line is simply x=0, which is a vertical line that passes through the y-axis at the point (0,2).
Note that the y=9+3x equation and its slope are irrelevant to this question because the given line x=9 is vertical and does not have a slope that we can describe with a number.