Question

The ordered pairs below represent a relation between x and y. (-3,-3), (-2,0), (-1,3), (0,6), (1,9), (2,12).
Could this set of ordered pairs have been generated by a liner function?
A. No, because the y-values decrease then increase
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it
C. No, because the distance between consecutive y-values is different than the distance between consecutive x-values
D. Yes, because the distance between x-values is inconstant

Answer 1

Notice that the first coordinates, -3, -2, -1, 0, 1, 2
are matched respectively to       -3,  0, 3, 6, 9, 12.

Thus, as the x-coordinate changes by 1, the y-coordinate changes by 3:

We can represent this change by the following picture:

         
                         |
                         |
            (2,12) _ |
                     |
                     |
         (1,9)  _ | 
                 |
                 |
     (0,6) _ |

                                                    
So, the points are on a straight line, because:

B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x,y) values you use to calculate it