I need help on some figuring out a way to write an equation from this table:

Number of Days Length

1 0.45 in.

4 1.80 in.

8 3.60 in.

Thanks!

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The first thing I always do in a table with two sets of values that seem to have a relationship to each other is look for patterns. I notice that all the length measurements, are multiples of 9 and a decimal, that could indicate a linear progression, if the ratio of days to length is the same for each data point. I write the ratios as fractions and I find:

`1/0.45=4/1.8=8/3.6=20/9` So these data points all form a straight line. I take two of the points (1, 0.45) and (4, 1.8) and determine an equation of y=mx+b. I find m by `(1.8-0.45)/(4-1)=0.45/3=0.15` So y=0.15x+b. I then plug in the x and y values from our third point (8, 3.6) to find b. `3.6=0.15(8)+b->3.6=3.6+b->b=0`

Your equation is `y=0.15x` or Length = 0.15 Days. From there you can re-arrange the terms into whatever format is requested.

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