1. **State the problem:** We are given the function $y = 2x - 3$ and a table with values of $x$ from $-3$ to $3$. We need to fill in the columns for $2x$ and $y = 2x - 3$. 2. **Formula used:** The function is $y = 2x - 3$. For each $x$, calculate $2x$ and then substitute into the formula to find $y$. 3. **Calculate $2x$ for each $x$:** - For $x = -3$, $2x = 2 \times (-3) = -6$ - For $x = -2$, $2x = 2 \times (-2) = -4$ - For $x = -1$, $2x = 2 \times (-1) = -2$ - For $x = 0$, $2x = 2 \times 0 = 0$ - For $x = 1$, $2x = 2 \times 1 = 2$ - For $x = 2$, $2x = 2 \times 2 = 4$ - For $x = 3$, $2x = 2 \times 3 = 6$ 4. **Calculate $y = 2x - 3$ for each $x$:** - For $x = -3$, $y = -6 - 3 = -9$ - For $x = -2$, $y = -4 - 3 = -7$ - For $x = -1$, $y = -2 - 3 = -5$ - For $x = 0$, $y = 0 - 3 = -3$ - For $x = 1$, $y = 2 - 3 = -1$ - For $x = 2$, $y = 4 - 3 = 1$ - For $x = 3$, $y = 6 - 3 = 3$ 5. **Final table values:** | $x$ | $2x$ | $y = 2x - 3$ | |-----|------|--------------| | -3 | -6 | -9 | | -2 | -4 | -7 | | -1 | -2 | -5 | | 0 | 0 | -3 | | 1 | 2 | -1 | | 2 | 4 | 1 | | 3 | 6 | 3 | This completes the table by calculating each value step-by-step.