Can I have some help please? If you can, please show your work so that I may better understand how to do this.

Question

One of the tables below contains (x,y) values that were generated by a linear function. Determine which table, and then write the equation of the linear function represented by the table.

 

Table #1: x: 2, 5, 8, 11, 14, 17, 20    

               Y: 1, 3, 7, 13, 21, 31, 43

 

Table #2 x: 1, 2, 3, 4, 5, 6, 7

              y: 10, 13, 18, 21, 26, 29, 34

 

Table #3 x: 2, 4, 6, 8, 10, 12, 14

              y: 1, 6, 11, 16, 21, 26, 31

Answer 1

I find it much easier to view tables of (x,y) this way:

 

Table #1:                         slope (this point with previous point)

             (2.1)

             (5,3)                         2/3

             (8,7)                         4/3

             (11,13)                     2

             (14,21)                      7/3

             (17,31)                      10/3

             (20,43)                       4

 

Table #2:                         slope (this point with previous point)

             (1,10)

             (2,13)                         3

             (3,18)                          5

             (4,21)                         3

             (5,26)                          5

             (6,29)                         3

             (7,34)                          5

 

Table #3:                         slope (this point with previous point)

               (2,1)

               (4,6)                         5/2

               (6,11)                       5/2

               (8,16)                       5/2

               (10,21)                     5/2

               (12,26)                     5/2

               (14,31)                     5/2

 

Note that Table #3 has the same slope regardless of which two points are chosen for the computation.

 

The slope-intercept form of the equation of a line looks like:    y = mx + b

     where    m = slope

                  b = y-intercept (the place where x=0)

 

Important:  The slope of a straight line is constant.  It may be computed using the coordinates of any two points on the line.

  That's why a line at be drawn using a ruler (or straight edge) to connect two points (and keep going in each direction).