1. **State the problem:** We are given the linear function $y = 3x + 3$ and a table of values for $x$ and $y$. We want to understand the relationship and verify the values. 2. **Formula used:** The function 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, $m = 3$ and $b = 3$. This means for every increase of 1 in $x$, $y$ increases by 3, and when $x=0$, $y=3$. 4. **Verify table values:** - 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 $x = 2$: $$y = 3(2) + 3 = 6 + 3 = 9$$ - For $x = 3$: $$y = 3(3) + 3 = 9 + 3 = 12$$ - For $x = 4$: $$y = 3(4) + 3 = 12 + 3 = 15$$ All values match the table. 5. **Explanation:** The function is linear with a constant rate of change (slope) of 3. The y-intercept is 3, meaning the line crosses the y-axis at (0,3). The points plotted correspond exactly to the function values. **Final answer:** The table correctly represents the function $y = 3x + 3$.