How to Find the Equation of a Line in the Plane

To find the equation of a line in the plane, we need to have a slope, and at least one point through which the line passes. This article will show by using an example How to Find the Equation of a Line in the Plane.

Things You'll Need

• Paper and
• Pencil

Instructions

1. 

   Given two points, P at coordinate (3,4) and Q at coordinate (7,2) we are going to find the Equation of the line that passes through the points P and Q. Please click on the image for better understanding.

2. 

   We must first find the Slope of the line that passes through the points P and Q. In order to find the Slope, we will use a formula which will also be given in the image. The Formula for the Slope is, M =(Y2-Y1)/(X2-X1). Which is M=(2-4)/(7-3) = -2/4. so M=-1/2. Please click on the image for better understanding.

3. 

   The formula for the Equation of a line in the plane that passes through two points is given as Y-Y1= M(X-X1) so, with the slope M= -1/2 and the points X1=3, Y1=4.
   We can now write the Equation as Y-4 = (-1/2)(X-3) which is equal to
   Y=(-1/2)(X-3) + 4. In simplified form, that is Y= (-1/2)X + 3/2 + 4 which is Y= (-1/2)X + 11/2. Please click on the image for better understanding.