1. **State the problem:** We have line $h$ with slope $\frac{3}{5}$ and x-intercept at $(17,0)$. Line $k$ is line $h$ translated down 4 units. We need to find the y-coordinate of the y-intercept of line $k$. 2. **Find the equation of line $h$:** The slope-intercept form is $y=mx+b$ where $m$ is slope and $b$ is y-intercept. 3. Use the x-intercept $(17,0)$ to find $b$: $$0=\frac{3}{5}\times 17 + b$$ $$0=\frac{51}{5} + b$$ $$b = -\frac{51}{5}$$ 4. So, equation of line $h$ is: $$y=\frac{3}{5}x - \frac{51}{5}$$ 5. **Translate line $h$ down 4 units:** This means subtract 4 from the $y$ values: $$y_k = y_h - 4 = \frac{3}{5}x - \frac{51}{5} - 4$$ 6. Simplify the constant term: $$-\frac{51}{5} - 4 = -\frac{51}{5} - \frac{20}{5} = -\frac{71}{5}$$ 7. Equation of line $k$ is: $$y = \frac{3}{5}x - \frac{71}{5}$$ 8. **Find y-intercept of line $k$:** Set $x=0$: $$y = \frac{3}{5} \times 0 - \frac{71}{5} = -\frac{71}{5}$$ **Final answer:** The y-coordinate of the y-intercept of line $k$ is $-\frac{71}{5}$ or $-14.2$.