When do two lines intersect

The point of intersection of two non- parallel lines can be found from the equations of the two lines. Try this Drag any of the 4 points below to move the lines.

Note where they intersect. Fig 1. Segments do not intersect. To make sure our calculations are correct, and also to demonstrate a point, we should get the same y-coordinate if we use the equation for Line 2. Let's try that:. Well, looks like everything has worked out.

The point of intersection for these two lines is 1. If you look back at the graph, this certainly makes sense:. Actually, there is nothing special about the functions being linear functions. This method could be used to find the point or points of intersection between many other types of functions. Here's a calculator to help you check your work. Make up two linear functions in slope-intercept form.

Calculate the point of intersection using the above methods. They cannot intersect at only one point because planes are infinite. Furthermore, they cannot intersect over more than one line because planes are flat. One way to think about planes is to try to use sheets of paper and observe that the intersection of two sheets would only happen at one line. A system of linear equations usually has a single solution, but sometimes it can have no solution parallel lines or infinite solutions same line.

Since parallel lines never cross, there can be no intersection; for a system of equations that graphs as parallel lines, there can be no solution. This is called an "inconsistent" system of equations, and it has no solution. Intersection of Two Lines Two distinct lines intersect at the most at one point.

Meaning of Intersection of Two Lines 2. Finding Intersection of Two Lines 3. The Angle of Intersection 4. Conditions for Two Lines to be Parallel or Perpendicular 5.