1. The problem is to graph the line given by the equation $$y = \frac{1}{5}x + 8$$ using the slope and y-intercept. 2. The slope-intercept form of a line is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. From the equation, the slope $m = \frac{1}{5}$ and the y-intercept $b = 8$. 4. The y-intercept means the line crosses the y-axis at the point $(0, 8)$. 5. The slope $\frac{1}{5}$ means for every increase of 5 units in $x$, $y$ increases by 1 unit. 6. Starting at $(0, 8)$, move 5 units to the right (to $x=5$) and 1 unit up (to $y=9$) to find another point on the line. 7. Plot these points and draw a straight line through them to graph the equation. Final answer: The line passes through points $(0,8)$ and $(5,9)$ with slope $\frac{1}{5}$.