The initial value is y when x is 0 — and these tables never print that row. These free printable worksheets find it by stepping the table back at its own rate.
If they get stuck
The answer key prints on a separate page.
No table on this sheet shows the x = 0 row, and that is deliberate: if it did, the answer would be a number to copy rather than one to work out. Finding the initial value means stepping backward from the first point at the table's own rate until x reaches 0 — which is why the rate has to be found first.
So the skill is really two moves in order. Read the rate of change off the table, then walk it back: if x = 2 gives y = 9 and the rate is 4, then x = 1 gives 5 and x = 0 gives 1. A child who tries to read the start straight off the table has nothing to read; a child who has the rate can always recover it.
One question from a sheet like this one, worked a step at a time — with a sentence saying what just happened and why.
Initial value from a table, step by step