1. **State the problem:** We are given two equations: $$y = 0.4 + 3.25$$ and $$y = 1.2x - 5.5$$ We want to compare these two equations using the comparison method. 2. **Simplify the first equation:** $$y = 0.4 + 3.25 = 3.65$$ So the first equation is actually a constant function: $$y = 3.65$$ 3. **Set the two expressions for $y$ equal to each other:** $$3.65 = 1.2x - 5.5$$ This is the key step in the comparison method: equate the two expressions for $y$ to find $x$. 4. **Solve for $x$:** Add $5.5$ to both sides: $$3.65 + 5.5 = 1.2x$$ $$9.15 = 1.2x$$ Divide both sides by $1.2$: $$x = \frac{9.15}{1.2}$$ Show cancellation: $$x = \frac{\cancel{9.15}}{\cancel{1.2}}$$ Calculate the division: $$x = 7.625$$ 5. **Find $y$ by substituting $x$ back into one of the equations:** Using the second equation: $$y = 1.2(7.625) - 5.5 = 9.15 - 5.5 = 3.65$$ 6. **Interpretation:** The two lines intersect at the point $(7.625, 3.65)$. This means the two equations are equal at this $x$ value. **Final answer:** $$x = 7.625, \quad y = 3.65$$