Intersection of lines

Introduction

We consider the intersection of two lines, and there are three cases (i) Lines with different gradients intersect at only one point (ii) Parallel lines do not intersect and (iii) lines that are indentical have an infinite number of intersection points. You can use the buttons to explore the three possible cases.

You can use the slider to find the intersection coordinate. The slider selects an x-value which is substituted into the equations to find the y-values. At the intersection point the y-value is the same for both lines:

Exercise: Find the intersection coordinate of these two lines

You can check you answer and working out below:

Summary

You can estimate the intersection point of two lines by plotting the lines. However, the exact intersection coordinate can be found algebraically.