What’s the rule for the translation (x, y) (x+3,y+7)

The rule would be right 3, since the algebraic composition is changing the x values, and up 7, since the y values are being changed. Whenever a number is being added to the x in the coordinate, the function is being moved to the right. When a number is subtracted from the x, then the function is moving left. 
For the y value, if you are adding a number to the y coordinate, you are moving it up, whereas when you subtract a number, you are moving it down that amount.