1. **State the problem:** We are given the linear equation $$y = -\frac{1}{3}x + 7$$ and want to understand how to interpret and work with it. 2. **Identify the form:** This equation is in slope-intercept form, which is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Explain the slope:** Here, the slope $m = -\frac{1}{3}$ means for every increase of 3 units in $x$, $y$ decreases by 1 unit. The negative sign indicates the line slopes downward. 4. **Explain the y-intercept:** The y-intercept $b = 7$ means the line crosses the y-axis at the point $(0,7)$. 5. **Plotting points:** To find points on the line, pick values for $x$ and calculate $y$. For example, when $x=0$, $$y = -\frac{1}{3} \times 0 + 7 = 7$$ so point $(0,7)$ is on the line. When $x=3$, $$y = -\frac{1}{3} \times 3 + 7 = -1 + 7 = 6$$ so point $(3,6)$ is on the line. 6. **Summary:** The line decreases by 1 unit in $y$ for every 3 units increase in $x$, crossing the y-axis at 7. This understanding helps graph the line or analyze its behavior.