1. **State the problem:** We are given a function rule $y = 6x - 1$ and a table with values of $x$. We need to find the corresponding $y$ values using the function. 2. **Formula:** The function rule is $y = 6x - 1$. This means for each $x$ value, multiply by 6 and then subtract 1 to get $y$. 3. **Calculate each $y$ value:** - For $x=1$: $$y = 6(1) - 1 = 6 - 1 = 5$$ - For $x=5$: $$y = 6(5) - 1 = 30 - 1 = 29$$ - For $x=6$: $$y = 6(6) - 1 = 36 - 1 = 35$$ - For $x=7$: $$y = 6(7) - 1 = 42 - 1 = 41$$ 4. **Fill in the table:** | x | y | |---|----| | 1 | 5 | | 5 | 29 | | 6 | 35 | | 7 | 41 | 5. **Explanation:** Each $y$ value is found by applying the function rule to the given $x$. This is a linear function with slope 6 and y-intercept -1, so the graph would be a straight line increasing by 6 units in $y$ for each increase of 1 in $x$. **Final answer:** The completed table is $\{(1,5), (5,29), (6,35), (7,41)\}$.