THE DRAGON THAT IS MATH


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SOLVING LINEAR EQUATIONS

In order to solve a linear equation, you must isolate the variable in the problem. Example:   2x-4x = -5    add the x's
                     -2x = -5   divide both sides by 2
                        x = 5/2 
Some linear equations have on solution.  For these problems you must state that they have no solution.  The reason for this is the number that x is multiplied by is 0.  0 multiplied by anything is zero, so 0 can not be equal to 32. Example:  5(x-4) = 5x+12  use distributive property
                5x-20 = 5x+12  add/subtract the x's and
                                          numbers
                0x = 32
                x has no possible solution
A final linear equation allows x to be any real number because x is equal to itself. Example:  2x = 2x             divide both sides by 2
                  x = x               x equals itself

 

SOLVING LITERAL EQUATIONS

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Literal equations are often forumlas which allow you to plug in the known variables to answer the problem.  They are often in the form of only letters. Example:  E = IR (Voltage formula)
Some involve multiplication. Example:  C = Q/V   You must multiply 
                                both sides by V to 
                                cancel V in Q/V
                CV = Q
Others involve division. Example:  E = IR      You must divide both
                                sides by R to cancel
                                the R in IR
                E/R = I

WRITING THE EQUATION OF A LINE

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The equation of a line can be written in three different forms.
The first form is point slope form.  It is written in the form of:    Y-Y1 = M(X-X1).
This is a base form for the other two.  X1 and Y1 are both coordinates.		 Example: Y-Y1 = M(X-X1)
               Y-12 = 2X + 4 
                                      If Y1=12 and X1=4
                                      then the equation 
                                      is solvable. The 
                                      slope must be 2.
The second form is Standard Form.  It is written in the form:     Y - MX = B                This is done so that the X and Y are on the same side of the equatio Example: Y - 2X = 4
               12 - 2(4) = 4     If Y=12 and X=4
                       4 = 4         then the equation
                                         is solvable. The
                                         slope must be 2.
The third form is Slope Intercept form and ins written in the form of:   Y = MX + B 
Where Y and X are equal to Y and X coordinates suitable for the equation.   M represents the slope of the line and B is the Y-intercept.		 Example:  Y = MX + B
                Y = 2X + 4      If Y=12 and X=4
                12 = 2(4) + 4   then the equation 
                12 = 12            is solvable. The 
                                        slope must be 2.

For further help, refer toMrs. Felz's website