how can you find a slope from a table

Question

How can you find a slope from a table. The y-claim and the x-claim

Answer 1

Take difference of Y ( vertical) Values divided by difference in X- values.

 

  If the relation is supposed to be linear, then the ratio has to be equal to all values of X and Y

 

   Example :

                  Cost of a plumbing vs number of hours of work is given in the following table:

           

            Hr       C

            1         50

                            20

            2        70

                           20  

           3        90

                          20

           4        110

 

     We see that the cost of every hr of work is $20

 

       70 -50  = 90- 70 = 110 -90  = 110 - 50  = 20

          1             1           1               3
    

    So the slope , rate of change( working extra 1 hour of work) is fixed, the relation ship is linera

 

 

      The equation of Cost vs number of hours of work is linear:

 

       C = 20 t + b             C is cost , and t is time in hour.

 

       to find b

 

       Plug one value of ( t, C ) in the equation:

 

      50 = 20( 1) + b

 

      b = 30

 

     Plug back to equation:

      C = 20t + 30

 

        $30 dollar is the Vertical intercept of the graph, it means cost of service call, then every hour of work

         costs $20 extra dollars.