Since you haven't given the initial coordinates of your original triangle, we need to assume some coordinates to answer the question.
Consider a triangle with vertices at the coordinates A(-1,1), B(1,1) nd C(2,1). Then the rule that is given requires that for every x-value, you add 3 to it, and for every y-value, you subtract 3 from it.
This means that A(-1,1) changes to D(-1+3,1-3)=D(2,-2).
Also, B(1,1) changes to E(1+3,1-3)=E(4,2).
Finally, C(2,1) changes to F(2+3,1-3)=F(5,-2).
Now, you can draw the original triangle ABC and the transformed triangle DEF on the same graph.
The new vertices are D(2,-2), E(4,2) and F(5,-2).