GENERAL FORM OF THE EQUATION FOR A LINEAR REALTION!

GENERAL FORM OF EQUATION!

Ax+By+C= 0

A is a whole number, and B and C are integers.



SOME RULES IN WRITING  IN STANDARD FORM INTO GENERAL FORM

• If the numberes are infraction, find the LCD first, then multiply the LCD to both sides.
• If it is in standard form, you just simply used the 'dig and transplant' method.
• The A value should always be positive.
• If the numbers has a fraction, multiply the denominator to both sides.

Rewriting an equation in General Form:
1.)   4x+3y=36
4x+3y-36=0

2.)  1/3y=5/6x-1/2
 (1st  step)2  6(1/3y)=(5/6x-1/2)6            (LCD:6... then multiply 6 to both sides!)
(2nd step)  2y=5x-3                                 (the answer in 1st step)           
 (collect all the terms on the left side of the equation)
  (3rd step) 5x-2y-3=0                             (This is the general form of the equation!)

3.) y=-2/3x=4
(1st step) 3(y)=3(-2/3x=4)                   (multiply each side by 3)
(2nd step) 3y=-2x=12                          (the answer in 1st step)
(collect all the terms on the left side of the equation)
(3rd step) 2x+3y-12=0                          (This is the general form of the equation!)

Determining the slope of a line given its equation in general form
3x-2y-16=0

(Rewrite the equation in slpoe- intercept form)

-2y-16=-3x     (1st step)
-2y-16=3x /-2  (2nd step)   (divide each side by -2)
y+8=3/2 (3rd step)
y=3/2 x-8

• The slope of the line is 3/2.

Determining the x and y intercept.

3x+2y-18=0

x-intercept:
( substitute y:0)
3x+2(0)-18=0
(solve for x)
3x=18
(divide both sides by 3)
3x/3 =18/3
x=6

y-intercept:
(substitute:0)
3(0)=2y-18=0
(solve for y)
2y=18
(divide each sides by 2)
2y/2 =18/2
y=9

General form into a equation.
8x-2y+10=0
(rewrite the equation into slope-intercept form)
-2y=-8x-10
(divide each side by -2)
-2y=-8x-10 /-2
y=4x+5
or
8x+10=2y /2
4x+5=y
y=4x+5