Line Graph A4377A

1. **State the problem:** We need to graph the line given by the equation $$y = \frac{1}{3} x - 3$$. 2. **Formula and explanation:** This is a linear equation 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 $$m = \frac{1}{3}$$ and the y-intercept $$b = -3$$. 4. **Plot the y-intercept:** The line crosses the y-axis at the point $$(0, -3)$$. 5. **Use the slope to find another point:** The slope $$\frac{1}{3}$$ means rise over run is 1 up for every 3 right. Starting at $$(0, -3)$$, move 3 units right to $$x=3$$ and 1 unit up to $$y=-2$$. 6. **Check the point:** Substitute $$x=3$$ into the equation: $$y = \frac{1}{3} \times 3 - 3 = 1 - 3 = -2$$. 7. **Draw the line:** Connect the points $$(0, -3)$$ and $$(3, -2)$$ with a straight line extending in both directions. **Final answer:** The graph is a straight line passing through $$(0, -3)$$ and $$(3, -2)$$ with slope $$\frac{1}{3}$$.