1. The problem is to create a table of values for the linear function $$y=\frac{1}{2}x+2$$. 2. The formula is $$y=\frac{1}{2}x+2$$, which means for each value of $x$, multiply by $\frac{1}{2}$ and then add 2 to get $y$. 3. Choose some values for $x$ to calculate corresponding $y$ values. Common choices are $x=-2, 0, 2, 4$. 4. Calculate $y$ for each $x$: - For $x=-2$: $$y=\frac{1}{2}(-2)+2=\cancel{\frac{-2}{2}}+2=-1+2=1$$ - For $x=0$: $$y=\frac{1}{2}(0)+2=0+2=2$$ - For $x=2$: $$y=\frac{1}{2}(2)+2=\cancel{\frac{2}{2}}+2=1+2=3$$ - For $x=4$: $$y=\frac{1}{2}(4)+2=\cancel{\frac{4}{2}}+2=2+2=4$$ 5. The table of values is: | $x$ | $y$ | |-----|-----| | -2 | 1 | | 0 | 2 | | 2 | 3 | | 4 | 4 | This table helps visualize the function by showing points on the line.