Review of Graphs and Slopes of Lines


     Example 1
     Find the slope of the line passing through    a)   (-8, 8), (6, -8)
                                                                                b)   (-7, 1), (-7, 0)

     Solution:      Using the formula of the slope which is  m =  

a)        m =    =  =                                  b)        m =  =  =  undefined

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      Example  2
      Find the slope and the y-intercept of the line      a)   3x – y = 9  
                                                                                       b)   X – 6 =19  
                                                                                       c)   Y - 2 = 0

Solution:  First solve the equation for y in order to have it written in the form y = mx + b, then pick the coefficient of x which is the slope; m  
a)  3x -y = 9       ð   -y = -3x + 9       ð   y =  3x - 9       ð   m = 3  
b)  x -6 = 19       ð   x = 25       ð   this is an equation for a vertical line where the slope is undefined.  
c)  y – 2 = 0       ð   y = 2        ð   this is an equation for a horizontal line where the slope is equal to zero.  
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      Example  3   
      Graph       a)   4x + 2y = 4                           b)     x + 2 = 0

      Solution:

To graph any linear equation we need at least two points:
a)   4x + 2y = 4

   x

y

  0

2

   1

0

Substitute x = 0 then y = 2   ð  (0, 2)

Substitute y = 0 then x = 1   ð  (1, 0)   



 b)  x + 2 = 0    ð   x = -2

x

y

-2

0

 -2

3

Substitute y = 0 then x = -2   ð  (-2 0)

Substitute y = 3 then x = -2   ð  (-2, 3)


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