1. **State the problem:** We are given the linear function $y = 3x + 4$ and a table with columns $x$, $3x$, and $y = 3x + 4$. We need to fill in the missing values in the table. 2. **Recall the formula:** The function is $y = 3x + 4$. For each $x$ value, calculate $3x$ and then $y$ by adding 4 to $3x$. 3. **Calculate $3x$ for each $x$:** - For $x = -3$, $3x = 3 \times (-3) = -9$ - For $x = -2$, $3x = 3 \times (-2) = -6$ - For $x = -1$, $3x = 3 \times (-1) = -3$ - For $x = 0$, $3x = 3 \times 0 = 0$ - For $x = 1$, $3x = 3 \times 1 = 3$ - For $x = 2$, $3x = 3 \times 2 = 6$ - For $x = 3$, $3x = 3 \times 3 = 9$ 4. **Calculate $y = 3x + 4$ for each $x$:** - For $x = -3$, $y = -9 + 4 = -5$ - For $x = -2$, $y = -6 + 4 = -2$ - For $x = -1$, $y = -3 + 4 = 1$ - For $x = 0$, $y = 0 + 4 = 4$ - For $x = 1$, $y = 3 + 4 = 7$ - For $x = 2$, $y = 6 + 4 = 10$ - For $x = 3$, $y = 9 + 4 = 13$ 5. **Fill in the table:** | $x$ | $3x$ | $y = 3x + 4$ | |-----|------|--------------| | -3 | -9 | -5 | | -2 | -6 | -2 | | -1 | -3 | 1 | | 0 | 0 | 4 | | 1 | 3 | 7 | | 2 | 6 | 10 | | 3 | 9 | 13 | This completes the table and shows how the function values are calculated step-by-step.