Question: Find the intersection point of the lines $ y = 3x + 4 $ and $ y = -2x + 19 $.

Wed, 06 May 2026 10:32:40 +0000

**Find the Intersection Point of the Lines $ y = 3x + 4 $ and $ y = -2x + 19 $**
In everyday life, data and trends often shape decisions—whether in budgeting, planning, or analyzing outcomes. The intersection of two lines on a graph reveals a critical balance: a single point where opposing forces meet. This concept resonates in many fields, from economics to personal finance, where understanding where variables align fuels clearer choices. Today, we explore the intersection of the equations $ y = 3x + 4 $ and $ y = -2x + 19 $—a mathematical intersection with practical relevance in problem-solving and decision-making across the U.S. **Why the Question Is Gaining Momentum in the US Market**
The intersection of linear equations often mirrors real-life crossroads: where multiple paths converge to a single outcome. Right now, more U.S. users are turning to clear, visual explanations of data relationships—especially in education, career planning, and skill development. This trend reflects growing interest in how to interpret and apply mathematical reasoning to everyday choices. The question “Find the intersection point of the lines $ y = 3x + 4 $ and $ y = -2x + 19 $” benefits from improved explainability and relevance to personal or professional growth, making it a rising topic in search visibility. **How to Find the Intersection: A Clear, Beginner-Friendly Approach**
The intersection of two lines is the only point where both equations produce the same $ y $-value for a given $ x $. To solve $ y = 3x + 4 $ and $ y = -2x + 19 $, set both expressions equal:
$ 3x + 4 = -2x + 19 $
Add $ 2x $ to both sides:
$ 5x + 4 = 19 $
Subtract 4:
$ 5x = 15 $
Divide by 5:
$ x = 3 $
Plug $ x = 3 $ back into either equation—say $ y = 3(3) + 4 = 13 $
The intersection point is $ (3, 13) $, where both lines meet and balance. **Common Questions About Finding Intersections**