Equations Made Easy


 

Lucky You!! We are starting with Linear Equations!!

   Problem:       4x + 5 = 25    You are solving for x
   1st Step:       4x + 5 = 25 
                             -5      -5		 You want to get all of your variables by themselves. So, you subtract 5 from BOTH sides. You should get  4x = 20
  Last Step:     4x = 20
                        4      4		 Still wanting to get the variable by itself, you divide by 4 on BOTH sides.  Your answer should be  x = 5!    GOOD JOB!

                                  Next we will solve Literal Equations!! 
 
 
 

   Problem:      m = ab + r     You are solving for b
    1st Step:      m = ab + r 
                       -r           -r		 Your goal is to get the variable you are trying to solve for by itself. So, first you subtract  r  from BOTH sides. You should get   m - r = ab.
    Last Step:   m - r = ab
                         a        a		 The last step you need to do is divide BOTH sides by  a. Your answer should be  m - r = b. 
                                        a

                                                          Did you get it? Good! Try these on your own!
 

1.          m = -a + th          solve for h answer:                m + a = h
                               t
2.          y = j - h               solve for j  answer:               y + h = j 
3.          g = ok                  solve for o answer:               g = o
                          k                                      GOOD JOB!


 

                                                                  Isn't  This Easy!?!
                                    C'mon! Lets learn some more!

                     Now you are going to learn the three ways to write an equation!!
                  ~ the first way you will learn is in standard form. It looks like this:      mx + y = b
                  ~ the second way you will learn is slope form. It looks like this:        y = mx +b
                  ~ the third way you will learn is point slope form. It looks like this:         y - y1 = m (x - x1)

                                                                          FYI:   y = point
                                                                                    m = slope
                                                                                    x = point
                                                                                    b = y intercept
ex.

   Standard form:    2x +2y =10     *change into slope form:     
   1st step:              2x + 2y = 10
                             -2x            -2x          		    2y = 2x + 10
 
   2nd step:             2y = 2x + 10
                              2           2		    y = 1x + 5
                               Ta Da!!! your answer is y = x +5

ex.

   Slope  form:      y = 2x + 10  * change to standard form:
   1st step:            y = 2x + 10
                         -2x   -2x     		 -2x + y = 10
   2nd step:       2x - y = -10    Since you can't have a neative at the begining, you are to divide by the negative.    You should get      2x - y = 10

ex.
                                                      for point slope form you have to substitute in points!!

  Point slope form:     y - y1 = m (x - x1)  * now put in the points (2,4) and (1,3)    solve
  1st step:                 4 - 3 = m (2 - 1)   you should get             1 = m(1)      

                                                            Well, you have learned all I can teach you!!
                                                                        If you like, you can view my school's web site!

                                                                      http://www.henry.k12.ga.us/ugh