1. **State the problem:** Rewrite the equation $$\frac{1}{2}x - \frac{3}{4}y = \frac{5}{6}$$ in the form $$y = mx + c$$ and find the gradient $$m$$. 2. **Formula and rules:** The slope-intercept form of a line is $$y = mx + c$$ where $$m$$ is the gradient (slope) and $$c$$ is the y-intercept. 3. **Isolate $$y$$:** Start with the given equation: $$\frac{1}{2}x - \frac{3}{4}y = \frac{5}{6}$$ Subtract $$\frac{1}{2}x$$ from both sides: $$- \frac{3}{4}y = - \frac{1}{2}x + \frac{5}{6}$$ 4. **Solve for $$y$$:** Multiply both sides by $$-\frac{4}{3}$$ to isolate $$y$$: $$y = \left(- \frac{4}{3}\right) \left(- \frac{1}{2}x + \frac{5}{6}\right)$$ 5. **Distribute:** $$y = \left(- \frac{4}{3}\right) \left(- \frac{1}{2}x\right) + \left(- \frac{4}{3}\right) \left(\frac{5}{6}\right)$$ 6. **Simplify each term:** $$y = \frac{4}{3} \times \frac{1}{2} x - \frac{4}{3} \times \frac{5}{6}$$ $$y = \frac{4}{6}x - \frac{20}{18}$$ 7. **Reduce fractions:** $$\frac{4}{6} = \frac{2}{3}$$ and $$\frac{20}{18} = \frac{10}{9}$$ 8. **Final equation:** $$y = \frac{2}{3}x - \frac{10}{9}$$ 9. **Gradient:** The gradient $$m$$ is the coefficient of $$x$$, which is $$\frac{2}{3}$$. **Answer:** The equation in slope-intercept form is $$y = \frac{2}{3}x - \frac{10}{9}$$ and the gradient $$m = \frac{2}{3}$$.