1. The problem is to graph the inequality $y < -\frac{1}{5}x - 1$. 2. This inequality represents all points below the line $y = -\frac{1}{5}x - 1$. 3. The line equation is $y = -\frac{1}{5}x - 1$, where the slope is $-\frac{1}{5}$ and the y-intercept is $-1$. 4. To graph the line, start at the point $(0, -1)$ on the y-axis. 5. From there, use the slope $-\frac{1}{5}$ which means for every 5 units you move to the right, move 1 unit down. 6. Draw a dashed line through these points because the inequality is strict ($<$), not including the line. 7. Shade the region below the line to represent all points where $y$ is less than $-\frac{1}{5}x - 1$. This completes the graphing of the inequality.