1. **State the problem:** We are given the linear function $$y = \frac{2}{3}x - 5$$ and a table with values of $$x$$: -9, 0, 3, 6. We need to find the corresponding values of $$y$$ (denoted as $$y'$$) for each $$x$$. 2. **Formula used:** The function is linear, so for each $$x$$, $$y$$ is calculated by substituting $$x$$ into the equation: $$y = \frac{2}{3}x - 5$$ 3. **Calculate each value:** - For $$x = -9$$: $$y = \frac{2}{3} \times (-9) - 5 = \frac{2 \times (-9)}{3} - 5 = \frac{-18}{3} - 5 = -6 - 5 = -11$$ - For $$x = 0$$: $$y = \frac{2}{3} \times 0 - 5 = 0 - 5 = -5$$ - For $$x = 3$$: $$y = \frac{2}{3} \times 3 - 5 = \frac{2 \times 3}{3} - 5 = \frac{6}{3} - 5 = 2 - 5 = -3$$ - For $$x = 6$$: $$y = \frac{2}{3} \times 6 - 5 = \frac{2 \times 6}{3} - 5 = \frac{12}{3} - 5 = 4 - 5 = -1$$ 4. **Summary:** The completed table is: | x | y' | |-----|-----| | -9 | -11 | | 0 | -5 | | 3 | -3 | | 6 | -1 | These values correspond to the output of the function for each input $$x$$. **Final answer:** $$y' = [-11, -5, -3, -1]$$