Final answer:
The equation that represents a line parallel to y = -3x + 4 is 6x + 2y = 15. So the correct answer is Option A.
Step-by-step explanation:
The equation of the line y = -3x + 4 has a slope of -3. To find a line that is parallel, we need to look for an equation that also has a slope of -3. Let's examine each option:
- a. 6x + 2y = 15: The equation can be rewritten as y = -3x + 7.5, meaning it has a slope of -3. This line is parallel to the given line.
- b. 3x - y = 7: The equation can be rewritten as y = 3x - 7, meaning it has a slope of 3. This line is not parallel to the given line.
- c. 2x - 3y = 6: The equation can be rewritten as y = (2/3)x - 2, meaning it has a slope of 2/3. This line is not parallel to the given line.
- d. x + 3y = 1: The equation can be rewritten as y = -1/3x + 1/3, meaning it has a slope of -1/3. This line is not parallel to the given line.
Therefore, the equation that represents a line parallel to y = -3x + 4 is a. 6x + 2y = 15.