1. **State the problem:** Find the slope of the line given by the equation $$4x - 1 = 3y + 5$$. 2. **Rewrite the equation in slope-intercept form:** The slope-intercept form is $$y = mx + b$$, where $$m$$ is the slope. 3. **Isolate $$y$$:** $$4x - 1 = 3y + 5$$ Subtract 5 from both sides: $$4x - 1 - 5 = 3y$$ $$4x - 6 = 3y$$ 4. **Divide both sides by 3 to solve for $$y$$:** $$y = \frac{4x - 6}{3}$$ Show cancellation step: $$y = \frac{\cancel{4x} - \cancel{6}}{\cancel{3}}$$ (Note: Here, no common factors to cancel between numerator and denominator, so this step is just to show division.) 5. **Rewrite as:** $$y = \frac{4}{3}x - 2$$ 6. **Identify the slope:** The coefficient of $$x$$ is the slope $$m = \frac{4}{3}$$. **Final answer:** The slope of the line is $$\frac{4}{3}$$, which corresponds to option A.