1. **State the problem:** We need to find the equation of line K that passes through the point $(15, 20)$ and is parallel to the line given by $$y = \frac{2}{5}x - 10.$$ 2. **Recall the formula and rules:** The slope-intercept form of a line is $$y = mx + c,$$ where $m$ is the slope and $c$ is the y-intercept. 3. **Identify the slope of the given line:** Since line K is parallel to the given line, it has the same slope. The slope of the given line is $$m = \frac{2}{5}.$$ 4. **Use the point-slope form to find $c$:** Substitute the point $(15, 20)$ and slope $m=\frac{2}{5}$ into the equation $$y = mx + c$$ to find $c$. $$20 = \frac{2}{5} \times 15 + c$$ 5. **Calculate:** $$20 = \frac{2}{5} \times 15 + c = \frac{2}{5} \times 15 + c = 6 + c$$ 6. **Solve for $c$:** $$c = 20 - 6 = 14$$ 7. **Write the equation of line K:** $$y = \frac{2}{5}x + 14$$ **Final answer:** $$y = \frac{2}{5}x + 14$$