1. **State the problem:** We need to find the equation of line K which is parallel to the line $y=\frac{2}{5}x - 10$ and passes through the point $(15, 20)$. 2. **Recall the formula:** The equation of a line in slope-intercept form is $y = mx + c$, where $m$ is the slope and $c$ is the y-intercept. 3. **Important rule:** Parallel lines have the same slope. Since line K is parallel to $y=\frac{2}{5}x - 10$, it has slope $m = \frac{2}{5}$. 4. **Use the point-slope form:** To find $c$, substitute the point $(x_1, y_1) = (15, 20)$ and slope $m=\frac{2}{5}$ into $y = mx + c$: $$20 = \frac{2}{5} \times 15 + c$$ 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:** $y = \frac{2}{5}x + 14$