The general equation of straight lines applies to all two-dimensional straight lines. Its basic form is ax+by+c = 0 (neither a nor b is zero). Because this feature is particularly suitable for describing straight lines in the computer field.

Knowledge expansion

It is known that two points p 1 (x 1, y 1) p2 (x2, y2) and P 1P2 on a straight line do not coincide.

For AX+BY+C=0:

When x 1=x2, the linear equation is x-x 1=0.

When y 1=y2, the linear equation is y-y 1=0.

When x 1≠x2, y 1≠y2, the slope of the straight line is k=(y2-y 1)/(x2-x 1).

Therefore, the linear equation is y-y1= (y2-y1)/(x2-x1) × (x-x1).

That is x2y-x1y-x2y1+x1= (y2-y1) x-x1(y2-y1).

That is, (y2-y1) x-(x2-x1) y-x1(y2-y1)+(x2-x1) y1= 0.

That is, (y2-y1) x+(x1-x2) y+x2y1-x1y2 = 0 ①.

It can be found that formula ① still holds when x 1=x2 or y 1=y2. So the general equation of the straight line AX+BY+C=0 is:

A=Y2-Y 1

B=X 1-X2

C=X2*Y 1-X 1*Y2 For more knowledge points, please pay attention to the mathematics series of general education in New Oriental Middle School of Beijing Normal University. I believe it can help you.