Equations of the line

In this video we will talk about different equations of the line. The first thing that must be clear to understand the equations of the line is how to define a line in the plane. To make a line, all we will need is two points represented in the plane. If we have two points, a line can pass through them.

In order to find the equations of the line first we will have to calculate the director vector from your two points. To do this, we will subtract. We will have to subtract the end coordinates minus the origin coordinates. Let's remember its formula:

Once we have the director vector We will begin to find the different equations of the line:

• vector equation: to make the vector equation we will have to apply the following formula:

• parametric equations: We will find them from the vector equation solving it as indicated below:

And this would give us:

• continuous equation: to find it we will have to solve for k (lambda). A) Yes:

• explicit equation of the line: To find it we will have to solve the y of the general equation: A) Yes:

Apart from these equations, we also have the equation that passes through two points and the equation point slope although I have not explained them because they are not so common.

To better understand these equations of the line I recommend that you watch the video. In addition, you can practice with our printable exercises with their solutions that I have left you on the web.