1. **State the problem:** We are given the linear equation $y = -\frac{1}{3}x + 2$ and want to understand its graph and key features. 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, $m = -\frac{1}{3}$ means the line falls 1 unit vertically for every 3 units it moves horizontally to the right. 4. **Y-intercept:** The line crosses the y-axis at $b = 2$, so the point $(0, 2)$ is on the graph. 5. **Plot points using slope:** Starting at $(0, 2)$, moving 3 units right to $x=3$, the $y$ value decreases by 1 to $y=1$, giving point $(3, 1)$. 6. **Check other points:** Similarly, moving left 3 units to $x=-3$, $y$ increases by 1 to $y=3$, point $(-3, 3)$. 7. **Graph description:** The line passes through points $(-6, 4)$, $(-3, 3)$, $(0, 2)$, and $(3, 1)$, confirming the slope and intercept. 8. **Summary:** The graph is a straight line with slope $-\frac{1}{3}$ and y-intercept 2, descending gently from left to right. **Final answer:** The line $y = -\frac{1}{3}x + 2$ has slope $-\frac{1}{3}$ and y-intercept 2, passing through points $(-6,4)$, $(-3,3)$, $(0,2)$, and $(3,1)$.