Question: Find the intersection point of the lines $y = 3x - 4$ (representing urban development growth) and $y = -2x + 16$ (modeling resource allocation).

Thu, 30 Apr 2026 07:51:54 +0000

**Find the intersection point of the lines $y = 3x - 4$ (representing urban development growth) and $y = -2x + 16$ (modeling resource allocation). What does this reveal about balancing progress and limits?** In an era of rapid urban expansion across U.S. cities, professionals are turning to data-driven insights to understand where growth meets practical limits. The intersection of two key lines—one reflecting development pressure, the other modeling constrained resource availability—offers a clear, visual way to grasp essential trade-offs shaping community planning, infrastructure investment, and sustainability efforts. For planners, policymakers, and engaged citizens, solving this equation reveals how urban momentum meets financial and spatial boundaries. **Why the Question Is Gaining Attention Across the U.S.**
Urban growth patterns continue to evolve amid rising population density, aging infrastructure, and ever-limited budgets. As metropolitan areas expand, decision-makers increasingly rely on simple yet powerful models to answer: Where are development opportunities most viable? When will current resources match demand? The intersection of $y = 3x - 4$ and $y = -2x + 16$ encapsulates this critical balance. Though not literal formulas, this pairing symbolizes a cost-growth equilibrium—where momentum meets financing and capacity. Online discussions highlight growing interest in effective resource deployment, especially as taxpayers and stakeholders seek transparency about how cities grow sustainably. **How It Actually Works: A Clear, Factual Explanation**
To find the intersection point, set the two expressions equal:
$3x - 4 = -2x + 16$
Solve for $x$:
$3x + 2x = 16 + 4$ → $5x = 20$ → $x = 4$
Substitute $x = 4$ into either equation to find $y$:
$y = 3(4) - 4 = 12 - 4 = 8$
So the intersection occurs at point $(4, 8)$. This mathematical point represents the balance: at $x = 4$ (representing, loosely, time, population scale, or projected investment), the combined forces of development growth ($y = 3x - 4$) meet allocated resources ($y = -2x + 16$). It’s a literal balance in modeling frameworks describing urban economics and planning trade-offs.