1. **State the problem:** We need to fill in the table for the equation $$y = -\frac{3}{4}x - 4$$ at the given values of $$x$$ and then graph the equation. 2. **Recall the formula:** The equation is in slope-intercept form $$y = mx + b$$ where $$m = -\frac{3}{4}$$ is the slope and $$b = -4$$ is the y-intercept. 3. **Calculate $$y$$ when $$x=0$$:** $$y = -\frac{3}{4} \times 0 - 4 = 0 - 4 = -4$$ 4. **Calculate $$y$$ when $$x=4$$:** $$y = -\frac{3}{4} \times 4 - 4 = -3 - 4 = -7$$ 5. **Fill in the table:** | x | y | |---|---| | 0 | -4 | | 4 | -7 | 6. **Summary:** The points to plot are $$(0, -4)$$ and $$(4, -7)$$. These points lie on the line described by the equation $$y = -\frac{3}{4}x - 4$$. This completes the table and prepares for graphing the line.