Adding a negative number is the same thing as subtracting a positive number. In fact, here are are two sample problems with positives written in. Normally we assume that a number is positive unless it is written as a negative.
+4 - +9 = -5 +4 + -9 = -5
The green dot represents the 4 in the problem. The red line represents the 9 in the problem (since it is nine units long). The red dot represents the answer to the problem. So, you can see that subtracting positive nine is the same as adding negative nine.
Here's another example:
+4 - +5 = -1 +4 + -5 = -1
The green dot represents the 4 in the problem. The red line represents the 5 in the problem (since it is five units long). The red dot represents the answer to the problem. As you can see, subtracting positive five is the same as adding negative five.