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How Does The Pattern Of Change For A Linear Relationship Show Up In A Table?

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Take a look at x values and determine if x values are growing/decreasing by a constant
do the same for y values

only if both x and y are growing/decreasing by a constant do you have a linear relationship
for example:

X: 1 2 3 4 5
y: -3 -1 1 3 5

x is increasing by 1 and y is increasing by 2 so it is a linear relationship
however,

x: 1 2 3 4 5
y: 1 2 4 8 10

here x is increasing by 1 by y is growing by a factor of 2 so it is not a linear relationship

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