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: ?

Answer 1

Table #1:

Using the first two points (2,1) and (5,3)

You get (x-2)/3 = (y-1)/2

But then the 3rd point (8,7) does not work, so this is not linear.

Table #2

Using the first two points (1,10) and (2,13)

You get x-1 = (y-10) /3

But then the 3rd point (3,18) does not work so this is also not linear.

Table #3

Using the first two points (2,1) and (4,6)

You get x-2 /2 = y-1 /5

And all the other points will work with this, which makes this table linear.

Rewrite the equation to get y = 5/2x-4