Ali's Math Help

 * Linear Equations *

A linear equation has one variable.
Equations are solved by producing string of equivalent equations until this variable is found. 
Solve 5n+7= 7n - 9   for n
5n+11 = 7n - 9
-11   -11
5n=7n - 20
                        -7  -7
-2n = -20
divide both sides by -2

n=10

 
 
Solve (3/7)x + 9 = 15 for x
-9     -9
(3/7)x = 6
Multiply all by 7 to kill fraction!
3x = 42
3      3 

x = 14


 

 

* Literal Equations *

Literal Equations have more than one variable. 
They are solved for a specific variable in terms of the other variables. 
You will never get a numerical answer, it will always contain a variable.
Example 1:
Solve 7x - 3y = 8 for y
-7x        -7x
-3y = 8 - 7x
divide both sides by -3
y= 8-7x
   -3
Example 2:
Solve 5xy+2 = z for y
m    
multiply by m to cancel fraction
5xy+2 = zm
                                         -2      -2
5xy = zm - 2
divide by 5x
y = zm - 2
                                             5x

 
 
 

* Writing the Equation of a Line *

There are three forms of the equation of a line:
1. Point-slope      y - y1 = m(x - x1)  when your y1 and x1 are the coordinates of a given point, and m is the slope. The y and x remain y and x, they are not subsituted with any numbers.

2. Slope-intercept     y = mx+b   where m is your slope, and b is your y intercept.

3. Standard form      ax+by = c   (where a and b are most often replaced by numbers)
 Example:   Write the equation of a line that passes through (3,2) and is perpindicular to y = - 3x+2 (Because it is perpindicular to the line, your slope will be positive 1/3---the opposite of -3)
**First do point-slope form:
Plug in your coordinates:    y+2 = 1/3(x+3)   
(the 2 is positive because y-(-2) makes it y+2)
**Now use that equation to get slope-intercept form:
     y+2 = 1/3(x+3)   =  
     y+2 = 1/3x +1   =  
        -2            -2     =  y= 1/3x+1
**Now use your slope-intercept form to get to standard:
    y = 1/3x +1
   -1/3x   -1/3x
   -1/3x - y = 1   Multiply all by -3 (to kill the fraction)
    (No fractions in standard form!) x - 3y = - 3  (change a negative x to a positive)
 
 
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