Explain why |−3| + |9| represents the distance between the points (−3, −5) and (9, −5).

Since -5 and -5 are the same number, they are on the same y axis so the only distance we need to calculate is between the X coordinates.

When looking for distance, you can not have a negative. what |-3|+|9| is looking for is the distance from 0 on the X axis. since distance can't be negative, (you go 3 miles away from your house in one direction, vs 3 miles in the opposite. both ways is positive, even with opposite directions. same with axis, it doesnt matter which way, only the number.) you need the absolute value of -3 to get the distance from the 0 on the x axis. 

short version: distance is positive, and its adding the distances from the x axis to get distance from each other