1. **State the problem:** We need to find the equation of a line $r$ in the $xy$-plane that has a slope of 4 and passes through the point $(0,6)$. 2. **Formula used:** The slope-intercept form of a line is given by: $$y = mx + b$$ where $m$ is the slope and $b$ is the $y$-intercept. 3. **Identify known values:** Here, the slope $m = 4$ and the line passes through $(0,6)$, which means the $y$-intercept $b = 6$ because when $x=0$, $y=b$. 4. **Write the equation:** Substitute $m=4$ and $b=6$ into the formula: $$y = 4x + 6$$ 5. **Check the options:** The equation matches option D. **Final answer:** The equation defining line $r$ is: $$y = 4x + 6$$