1. **State the problem:** We have line C with equation $y=4x-1$ and line D is perpendicular to line C. They intersect at point $(1,3)$. We need to find the equation of line D. 2. **Recall the slope rule for perpendicular lines:** If two lines are perpendicular, the slope of one line is the negative reciprocal of the other. The slope of line C is $4$, so the slope of line D is $-\frac{1}{4}$. 3. **Use point-slope form:** The equation of a line with slope $m$ passing through point $(x_1,y_1)$ is $$y - y_1 = m(x - x_1)$$ Here, $m = -\frac{1}{4}$ and $(x_1,y_1) = (1,3)$. 4. **Substitute values:** $$y - 3 = -\frac{1}{4}(x - 1)$$ 5. **Simplify:** $$y - 3 = -\frac{1}{4}x + \frac{1}{4}$$ 6. **Add 3 to both sides:** $$y = -\frac{1}{4}x + \frac{1}{4} + 3$$ 7. **Combine constants:** $$y = -\frac{1}{4}x + \frac{1}{4} + \frac{12}{4} = -\frac{1}{4}x + \frac{13}{4}$$ **Final answer:** $$y = -\frac{1}{4}x + \frac{13}{4}$$