1. **State the problem:** We need to complete the table for the equation $$y = -x + 1$$ by finding the corresponding $$y$$ values for $$x = -2, 0, 1$$. 2. **Formula used:** The equation of the line is $$y = -x + 1$$. This means for any value of $$x$$, $$y$$ is calculated by negating $$x$$ and then adding 1. 3. **Calculate each value:** - For $$x = -2$$: $$y = -(-2) + 1 = 2 + 1 = 3$$ - For $$x = 0$$: $$y = -(0) + 1 = 0 + 1 = 1$$ - For $$x = 1$$: $$y = -(1) + 1 = -1 + 1 = 0$$ 4. **Complete the table:** | x | y | |---|---| | -2 | 3 | | 0 | 1 | | 1 | 0 | 5. **Explanation:** The line has a slope of $$-1$$, meaning it goes down 1 unit for every 1 unit it moves to the right. The y-intercept is 1, so the line crosses the y-axis at $$y=1$$. The completed table helps us plot the points $$(-2,3)$$, $$(0,1)$$, and $$(1,0)$$ to graph the line accurately.