1. **State the problem:** We need to find the equations that model the locus of the line graphed on the coordinate plane, given $d=3.5$ and a horizontal line segment at $y=2$. 2. **Understand the locus of a line:** A horizontal line at $y=2$ means every point on the line has the same $y$-coordinate, which is 2. 3. **Equation of a horizontal line:** The general form is $y = c$, where $c$ is a constant. Here, $c=2$, so the equation is: $$y = 2$$ 4. **Check the options given:** - $x = -1.5$ and $y = 5.5$ (vertical and horizontal lines at different values) - $y = 5.5$ and $y = -1.5$ (two horizontal lines) - $y = 5.5$ and $x = -1.5$ (horizontal and vertical lines) - $x = 5.5$ and $x = -1.5$ (two vertical lines) None of these match the line at $y=2$. 5. **Conclusion:** The locus of the line graphed is modeled by the equation: $$y = 2$$ This is a single horizontal line, not a pair of lines as in the options. **Final answer:** $$y = 2$$