Final answer:
The equation that represents a line parallel to y = -3x + 4 is (a) 6x + 2y = 15, after it is transformed into slope-intercept form y = -3x + 7.5, which has the same slope of -3.
Step-by-step explanation:
The question asks which of the following equations represents a line that is parallel to the line with the equation y = -3x + 4. To find a line that is parallel, we need to look for an equation with the same slope, since parallel lines have identical slopes. The original line has a slope of -3. Transforming each choice to the slope-intercept form (y = mx + b), where m is the slope, we find:
- For 6x + 2y = 15, if we solve for y, we get y = -3x + 7.5.
- For 3x - y = 7, if we solve for y, we get y = 3x - 7.
- For 2x - 3y = 6, if we solve for y, we get y = (2/3)x - 2.
- For x + 3y = 1, if we solve for y, we get y = -(1/3)x + (1/3).
The only equation with a slope of -3 is the first one: 6x + 2y = 15, which simplifies to y = -3x + 7.5. Thus, the answer is (a) 6x + 2y = 15.