1. **State the problem:** We need to graph the linear equation $$y = 1 + \frac{4}{5}x$$ and fill in the table for given values of $x$. 2. **Formula and rules:** The equation is in slope-intercept form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate $y$ when $x=0$:** $$y = 1 + \frac{4}{5} \times 0 = 1 + 0 = 1$$ 4. **Calculate $y$ when $x=5$:** $$y = 1 + \frac{4}{5} \times 5 = 1 + \frac{4}{5} \times 5$$ Show intermediate cancellation: $$y = 1 + \cancel{\frac{4}{5} \times 5} = 1 + 4 = 5$$ 5. **Fill the table:** | x | y | |---|---| | 0 | 1 | | 5 | 5 | 6. **Graph shape:** The graph is a straight line with slope $\frac{4}{5}$ and y-intercept $1$. It passes through points $(0,1)$ and $(5,5)$. Final answer: The table values are $y=1$ when $x=0$ and $y=5$ when $x=5$.