1. The problem asks us to find the slope-intercept form of a line with slope $\frac{5}{6}$ passing through the point $(12,4)$. 2. Recall the slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Substitute the slope $m = \frac{5}{6}$ and the point $(x, y) = (12, 4)$ into the equation to solve for $b$: $$4 = \frac{5}{6} \times 12 + b$$ 4. Calculate $\frac{5}{6} \times 12$: $$\frac{5}{6} \times 12 = 5 \times 2 = 10$$ 5. Substitute back to find $b$: $$4 = 10 + b \Rightarrow b = 4 - 10 = -6$$ 6. The slope-intercept form of the line is: $$y = \frac{5}{6}x - 6$$