**Nanako, from Japan, changes a graph, but
keeps the equation the same, HOW?!**

**Don
started Nanako on graphing linear equations, specifically x+y=8
below, because she is
8 years old. She picked up the plotting points quickly and proceeded to find
pairs of numbers with negatives numbers, like 9+ ^{-}**

**
Then Don asked her to change one thing in the
equation, like x+y=4; what would the graph look like? She said it would be
smaller (whatever she meant, I wasn't sure). She proceeded to graph this
equation above. Don told her that the lines will never meet and are parallel.
Again Don asked her to change something in the equation. This time she said she
would try to get a line that went like this / instead of like \. She said she
would move the y-axis to the right, and she proceeded to make the negative numbers on the
x-axis go down to the right, and the positive numbers get bigger to the left!!!
Don had never seen anyone do this before, he was very excited! Here is her graph
using the same equation:**

**That's exactly what
she was trying to do! WOW!! Don asked Nanako how she came to do this, and after
thinking about that, she said, "it just popped into my head"!**

**Don went over the
fact that a point like (2,2) marked with the x, was not on the line and the pair
of numbers do not make the sentence true, 2+2 = 8 is False. Only the pairs of
numbers that make x+y=8 true, will be on that line.**

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