1. **State the problem:** We have parallelogram WXYZ with side WX having equation $$y=\frac{1}{4}x - 6$$. We need to find the equation of segment YZ, which passes through point $(-1,5)$ and is parallel to WX. 2. **Recall the property of parallelograms:** Opposite sides are parallel, so YZ is parallel to WX. 3. **Find the slope of WX:** From the equation $$y=\frac{1}{4}x - 6$$, the slope is $$m=\frac{1}{4}$$. 4. **Since YZ is parallel to WX, slope of YZ is also $$\frac{1}{4}$$.** 5. **Use point-slope form for YZ passing through $(-1,5)$:** $$y - y_1 = m(x - x_1)$$ where $$m=\frac{1}{4}$$, $$x_1=-1$$, $$y_1=5$$. 6. **Substitute values:** $$y - 5 = \frac{1}{4}(x - (-1))$$ 7. **Check the options:** This matches the first option: $$y - 5 = \frac{1}{4}(x + 1)$$ **Final answer:** $$\boxed{y - 5 = \frac{1}{4}(x + 1)}$$