1. **State the problem:** Find the intersection point of the lines given by the equations $y=4x$ and $y=1.5x+12.5$. 2. **Set the equations equal:** At the intersection, the $y$ values are the same, so set $4x = 1.5x + 12.5$. 3. **Solve for $x$:** $$4x = 1.5x + 12.5$$ Subtract $1.5x$ from both sides: $$4x - 1.5x = 12.5$$ $$\cancel{4x} - \cancel{1.5x} = 12.5$$ $$2.5x = 12.5$$ 4. **Divide both sides by 2.5:** $$x = \frac{12.5}{2.5}$$ $$x = 5$$ 5. **Find $y$ by substituting $x=5$ into one of the original equations:** Using $y=4x$: $$y = 4 \times 5 = 20$$ 6. **Conclusion:** The lines intersect at the point $(5, 20)$.