1. The problem asks us to write the equation of a line in slope-intercept form given the slope and y-intercept. 2. The slope-intercept form of a line is given by the formula: $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = \frac{1}{5}$ and the y-intercept $b = -10$. 4. Substitute these values into the formula: $$y = \frac{1}{5}x + (-10)$$ 5. Simplify the equation: $$y = \frac{1}{5}x - 10$$ 6. This is the equation of the line in slope-intercept form. Final answer: $$y = \frac{1}{5}x - 10$$