1. **State the problem:** Find the equation of a line passing through the point $(2,8)$ and parallel to the line segment $GH$. 2. **Identify the slope of line $GH$:** The line $GH$ goes from point $G$ (upper left) to point $H$ (lower center). Assuming coordinates for $G$ and $H$ based on the description (e.g., $G=(0,y_G)$ and $H=(x_H,0)$), the slope $m_{GH}$ is calculated by $$m_{GH} = \frac{y_H - y_G}{x_H - x_G}$$ Since $G$ is upper left and $H$ is lower center, the slope is negative. 3. **Use the point-slope form:** The equation of a line parallel to $GH$ passing through $(2,8)$ has the same slope $m_{GH}$: $$y - 8 = m_{GH}(x - 2)$$ 4. **Simplify the equation:** Expand and rearrange to slope-intercept form $y=mx+b$. 5. **Final answer:** The equation of the line parallel to $GH$ through $(2,8)$ is $$y = m_{GH}x + b$$ where $b$ is found by substituting $x=2$, $y=8$. Since exact coordinates of $G$ and $H$ are not given, the slope cannot be numerically calculated here, but the method is as above.