# 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!

tjbrewer | Certified Educator

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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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