1. **Stating the problem:** Convert the equation $5x + 4y = 12$ into the slope-intercept form $y = mx + c$ and find the y-intercept. 2. **Formula and rules:** The slope-intercept form of a line is given by: $$y = mx + c$$ where $m$ is the slope and $c$ is the y-intercept. 3. **Rearranging the equation:** Start with the given equation: $$5x + 4y = 12$$ Subtract $5x$ from both sides: $$\cancel{5x} + 4y - \cancel{5x} = 12 - 5x$$ which simplifies to: $$4y = 12 - 5x$$ 4. **Isolating $y$:** Divide both sides by 4: $$y = \frac{12 - 5x}{4} = \frac{12}{4} - \frac{5x}{4}$$ 5. **Simplify the fractions:** $$y = 3 - \frac{5}{4}x$$ Rewrite in slope-intercept form: $$y = -\frac{5}{4}x + 3$$ 6. **Identify the y-intercept:** The y-intercept $c$ is the constant term when $x=0$, which is: $$c = 3$$ **Final answer:** $$y = -\frac{5}{4}x + 3$$ The y-intercept is $3$.