1. **State the problem:** We are given the linear equation $y = -3x + 12$ and want to understand its properties. 2. **Formula and rules:** This is a linear function in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, the slope $m = -3$ and the y-intercept $b = 12$. 4. **Find x-intercept:** Set $y=0$ to find the x-intercept: $$0 = -3x + 12$$ $$3x = 12$$ $$x = \cancel{\frac{12}{3}} = 4$$ 5. **Interpretation:** The line crosses the y-axis at $(0,12)$ and the x-axis at $(4,0)$. The slope $-3$ means the line falls 3 units vertically for every 1 unit it moves horizontally to the right. 6. **Summary:** The function $y = -3x + 12$ is a straight line with slope $-3$, y-intercept $12$, and x-intercept $4$.