Final answer:
Two lines are parallel if they have the same slope. Based on the line equation y = 9 + 3x with a slope of 3 and containing point C (3,4), the parallel line's equation is y = 3x - 5. However, this equation is not listed in the options given by the student.
Step-by-step explanation:
The student is asking for the equation of a line that is parallel to a given line and passes through a specific point C (3,4). Two lines are parallel if they have the same slope. Since the slope (m) is not provided for the original line, we cannot directly select an answer from the options given. However, if we infer from the additional reference provided that the original line's equation is y = 9 + 3x, which has a slope of 3. To find the equation of a line that is parallel to this and passes through the point (3,4), we would use the known slope (3) and the given point to write the equation using the point-slope form which is y - y1 = m(x - x1). Upon substituting the values, we get y - 4 = 3(x - 3). Simplifying this, we get y = 3x - 5. Unfortunately, this equation is not listed among the answer options provided, which suggests there may be an error in the question or the information provided by the student.