POINT OF DISCONTINUITY POINT OF INTERSECTION
Definition Of Point Of Discontinuity
The point at which two or more lines intersect is called the Point of Intersection.
More About Point of Discontinuity
Two lines always intersect at only one point.
The point of intersection also gives the solutions for a system of equations.
Video Examples: MATH - Points of Intersection
Example of Point of Discontinuity
The point of intersection of two lines x - y = 0 and 3x - 10y = - 14 is given below.
P(2, 2) is the point of intersection for the above system and also is the solution of the given systems of equations.
Solved Example on Point of Discontinuity
Ques: Identify the graph that represents the point of intersection of the two given lines and spot the point of intersection.
2x - y = 4
3y - x = 3
Choices:
A. Graph 1; (3, 2)
B. Graph 2; (- 2, 0)
C. Graph 3; (2, 3)
D. Graph 4; (4, 4)
Correct Answer: A
Solution:
Step 1: The point at which two or more lines intersect is called the Point of Intersection.
Step 2: Plot the given equations on a graph.
Step 3: The point of intersection from in the graph is (3, 2).
Step 4: So, Graph 1 represents the two given lines and the point of intersection is (3, 2).
Quick Summary
- Two lines intersect at only one point (in a 2D plane unless parallel or coincident).
- The point of intersection represents the solution to the system of equations formed by the intersecting lines.
🍎 Teacher Insights
Emphasize the connection between graphical representation and algebraic solutions. Use real-world examples to illustrate the concept of intersection.🎓 Prerequisites
- Linear equations
- Graphing linear equations
- Solving systems of equations
Check Your Knowledge
Q1: What is the point of intersection of the lines y = x and y = -x + 2?
Q2: The point of intersection of two lines represents:
Frequently Asked Questions
Q: How do I find the point of intersection?
A: Solve the system of equations represented by the lines. This can be done graphically or algebraically (substitution, elimination).
Q: What if the lines are parallel?
A: Parallel lines do not intersect, so there is no point of intersection. The system of equations has no solution.