Math in the Morning ...
(or whenever)
Shannon's Algebra II page for fellow mathematicians
 Hey ya'll!  This Georgia gal's gonna do her best to clear up any problems 
you may have about how to solve linear equations, literal equations, and 
how to write an equation for a line in three forms!
Prepare yourself to enter the world of numbers and letters please!
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* LINEAR EQUATIONS- (single variable) is an equation that can be written in the form of ax = b when 
a and b are constants and a does not equal 0.  So its a solve for x deal.  Easy huh??  Well, 
sometimes they can look kinda messy... here are two examples of what might look threatening, but can, and will, be tamed.
EXAMPLE 1- PARENTHESES AND BRACKETS
  
t = 2 - 2 [2t - 3 (1-t)]
parentheses and brackets make this appear evil, but if you distribute the -3...
t = 2 - 2 [2t - (3 + t)]
and then multiply the 2t by the -2 and drop the brackets and parenthesis...
t = 2 - 4t - 3 + t
now you combine like terms...
t = -3t-1
now solve for t!  wasn't that simple?
4t = -1
divide for you variable...
t = -.25
You're Done!

 
EXAMPLE 2- FRACTIONS
  
(P/3) + (3/4P) = [9/2(P-1)]
can we do something to tone this down?  You bet!  Let's distribute the (9/2)
(P/3) + (3/4)P = (9/2)P-(9/2)
KILL THE DENOMINATORS!  (Find your Lowest Common Denominator)
4P + 9P = 54P - 54
This is what you should get after multiplying by your LCD, which was 12
13P = 54P-54
Combine like terms...
-41P = -54
multiply by a negative 1 to create a positive equation...
41P = 54
solve for P!
P = 1.317
Wasn't that EASY??

Literal Equation - an equation created simply with letters.  So it's a scientific formula right?  All you have to do is move around some letters to find the one you want-- it's really simple- hang in there!
 
 
 
 
LITERAL EQUATIONS
  
SOLVE for p          p + E/V = k,
this is a simple literal equation, nothing to fancy, just get rid of the E/V by multiplying both sides by the reciprocal (V/E)
p = (V/E) * k
Now you have solved a literal equation!  Simple huh??





  
Now we get to dive into the equation of a line ... in all three forms!  we'll cover standard form, point slope, and slope intercept.

 

SLOPE INTERCEPT 
this is the traditional y = mx + b equation.  lets say that out points are (0,1) and (2,3)
 (3 - 1)/(2 - 0)     2/2 = 1     m = 1
difference in y divided by the difference in x.  this gives you the slope, or m in the equation 
 3 = 2(1) + b
pick an ordered pair and use it's points for the x and y to find the b 
 3 = 2 + b     3 - 2 = b     1 = b
simplify and isolate the variable! 

 
POINT SLOPE
the formula for a point slope problem is y* - y1 = m(x* - x 1)  the stars are just for you to identify that these letters do not change.  lets have our point be (2,8), and the slope is 4
y - 8 = 4(x - 2)
insert your x, y and m.  work it out!
y - 8 = 4x - 8
here's your point slope form!

 
 
 
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