1. The problem asks for the slope of the line given by the equation $$4x - 1 = 3y + 5$$. 2. To find the slope, we need to rewrite the equation in slope-intercept form $$y = mx + b$$, where $$m$$ is the slope. 3. Start by isolating $$y$$: $$4x - 1 = 3y + 5$$ Subtract 5 from both sides: $$4x - 1 - 5 = 3y$$ $$4x - 6 = 3y$$ 4. Divide both sides by 3 to solve for $$y$$: $$y = \frac{4x - 6}{3} = \frac{4}{3}x - 2$$ 5. From the slope-intercept form, the slope $$m = \frac{4}{3}$$. 6. Therefore, the correct answer is A: $$\frac{4}{3}$$.