1. **Problem statement:** We are given the equation $$y = 3x + 3$$ and asked to: (a) Create a table of y-values for $$x = -2, -1, 0, 1, 2$$. 2. **Formula and explanation:** The equation $$y = 3x + 3$$ is a linear equation in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Calculate y-values:** Substitute each x-value into the equation: - For $$x = -2$$: $$y = 3(-2) + 3 = -6 + 3 = -3$$ - For $$x = -1$$: $$y = 3(-1) + 3 = -3 + 3 = 0$$ - For $$x = 0$$: $$y = 3(0) + 3 = 0 + 3 = 3$$ - For $$x = 1$$: $$y = 3(1) + 3 = 3 + 3 = 6$$ - For $$x = 2$$: $$y = 3(2) + 3 = 6 + 3 = 9$$ 4. **Table of values:** | x | y | |----|----| | -2 | -3 | | -1 | 0 | | 0 | 3 | | 1 | 6 | | 2 | 9 | 5. **Interpretation:** The equation is linear because it is in the form $$y = mx + b$$ and the graph of these points will form a straight line. 6. **Summary:** The y-values for the given x-values are $$-3, 0, 3, 6, 9$$ respectively, confirming the linear relationship. Final answer: The equation $$y = 3x + 3$$ is linear and the table of values is as shown above.