Reduction of General Equation

Introduction 

The general equation is presented by the equation between two variables that represents a straight line on a graph. The equation of general form is Ax + By + C = 0.  The reduction form of the general equation is considered with the equation in x and y. It is Ax + By + C = 0. This equation can be written as By = -Ax – C, on the other hand, reduction in double intercept form is different from previous equations, in this respect the equation can be written as Ax+By = -C.

Discussion

Properties of “reduction of the general equation”    

• The concept of reduction in slope intercept form is considered in the first-degree general equation where the equation can be written as By = -Ax – C, or y=(-A/B)x+(-C/B) it is considered as the form of y=mx+c. In this respect the slope (m) = -A/B = -coefficient of x/coefficient of y. On the other hand y-intercept (C) = -C/B = content term/coefficient of B
• The reduction can also be performed in double intercept form, in this respect the equation can be written as Ax+By = -C, in this case while dividing both sides by -C comes with the result Ax/-C+Bx/-C = 1, on the other hand, x/ -C/A + y/-C/B = 1, it can be considered as the form of x/a +y/b = 1, 
• In the case of the second-order equation there is consideration of x2y ′′ − 3xy′ + 4y = 0 in this reduction of order method, the first coefficient is x2 and it vanishes when the x stands for 0.  In this respect x = 0 is not ought to be internal or intersect, as the result solving over the intervals shall be (0,∞) and (−∞, 0). 

The concept of reduction of normal equations is considered as the equation where x cosΦ p represents the one and singular straight line if the correspondent’s coefficients are proportional. In this case, cosΦ/A = SinΦ/B = -p/C = K. The general idea of reduction of line of the equation is a0 y (N) + a1 y (N−1) + · · · + aN−2 y ′′ + aN−1 y ′ + aN y = g, it is basically known as a trivial solution where y1 = y1 (x).

• One solution of x 2 y ′′ − 3xy′ + 4y = 0 this solution can be considered as ay′′ + by′ + cy = 0, in this equation the a,b and c are known functions where a(x) can never be zero. The reduction of the normal form of equation of straight line can be considered as (Ak)2+(Bk)2 = cos2Φ + sin2Φ= 1

• The reduction in slope intersects formula is considered as the m = -coefficient of x/coefficient of y, in this formation the transformation of the equations is considered as the equation of straight-line where 2x + 3y – 9 = 0 while reducing the equation in this formula -5x + 2y = 7, according to the formula the slope of the given straight lines, in this respect 5/2 and y-intercept shall be 7/2.    
• There is the consideration of arbitrary constant from c1 and c2 and B and A, in this respect, the reductio order is consisted by ay′′ + by′ + cy = g, in this homo-genopussi equation, the correspondence of y1 is considered as ay′′ + by′ + cy = 0

Types of “reduction of the general equation”

There are certain types of reduction that can be operated by the general equation of straight lines. There are considerations of slope intersection form, the formula of reduction in this form is ax + by + c = 0. ⇒ x−ca + y−cb = 1, in this formula there is consideration of intersection forms such as (xa + yb = 1). In this slope intercept form, the general equation Ax + By + C = 0, is encountered into the slope-intercept form and the result of the general equation shal be Ax + By + C = 0. ⇒ y= – A/Bx – C/B .There are other considerations of point-slope form, in this perspective the equation of reduction is y – y1 = m * (x – x1)

Examples of “reduction of the general equation”

In the different standard from the reduction of the general equation is considered as Ax+By+C=0, where the form of y = mx+c in this respect the given equation is Ax+By+C=0⇒y=-A/B, C=−C/B(B≠0). The intercept form is another aspect of the reduction of the general equation. In this respect, the form x/a+y/b = 1 is established where the reduction is possible only at a certain time when C is not equal to zero.

Conclusion 

In conclusion, it can be considered that the general form of equation in the case of straight lines has certain limitations as the result; a reduction from double intercept form is highlighted. It also depends on the length of the perpendicular from a point of a straight line.