Notice that if we start with x = 1 and increase x by 1, we get 2. Simultaneously, y starts with -1 and becomes 3. Thus, the slope is m = rise / run = 4/1, or 4.
The rule is y = 4x - 5.
Check: Suppose we pick input 4 from the table. Does this rule produce output 11? Is 11 = 4(4) - 5 true? YES.