1. The problem asks us to find which equation represents a line parallel to the line given by $$y = -3x + 4$$. 2. Recall that parallel lines have the same slope. 3. The slope of the given line is $$-3$$ (coefficient of $$x$$ in slope-intercept form $$y=mx+b$$). 4. We need to find which equation among the options has slope $$-3$$ when rewritten in slope-intercept form. 5. Let's analyze each option: A) $$6x + 2y = 15$$ Solve for $$y$$: $$2y = -6x + 15$$ $$y = -3x + \frac{15}{2}$$ Slope is $$-3$$, matches the given slope. B) $$3x - y = 7$$ Solve for $$y$$: $$-y = -3x + 7$$ $$y = 3x - 7$$ Slope is $$3$$, does not match. C) $$2x - 3y = 6$$ Solve for $$y$$: $$-3y = -2x + 6$$ $$y = \frac{2}{3}x - 2$$ Slope is $$\frac{2}{3}$$, does not match. D) $$x + 3y = 1$$ Solve for $$y$$: $$3y = -x + 1$$ $$y = -\frac{1}{3}x + \frac{1}{3}$$ Slope is $$-\frac{1}{3}$$, does not match. 6. Only option A has slope $$-3$$, so it represents a line parallel to the given line. Final answer: A) $$6x + 2y = 15$$