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9-84.

Identify the type of growth in each table below as linear or non-linear.

Linear growth forms a line when the data points are graphed. On a table, you can tell if growth is linear by checking if the $y$-values increase at a constant rate

1.  $x$ x column 1 $-2$ x column 2 $-1$ x column 3 $0$ x column 4 $1$ x column 5 $2$ x column 6 $3$ $y$ y column 1 $-8$ y column 2 $-1$ y column 3 $0$ y column 4 $1$ y column 5 $8$ y column 6 $27$

When $x$ increases by $1$, does $y$ increase by a specific amount? If it helps, take the data points and plot them on a graph.

This table shows non-linear growth. $y$ does not increase at a consistent rate, and the points on the graph do not form a line.

2.  $x$ x column 1 $-2$ x column 2 $-1$ x column 3 $0$ x column 4 $1$ x column 5 $2$ x column 6 $3$ $y$ y column 1 $4$ y column 2 $6$ y column 3 $8$ y column 4 $10$ y column 5 $12$ y column 6 $14$

See the help for part (a).

This table shows linear growth. Make sure you are able to explain why.

3.  $x$ x column 1 $-2$ x column 2 $-1$ x column 3 $0$ x column 4 $1$ x column 5 $2$ x column 6 $3$ $y$ y column 1 $\frac { 1 } { 4 }$ y column 2 $\frac { 1 } { 2 }$ y column 3 $1$ y column 4 $2$ y column 5 $4$ y column 6 $8$

See the help for part (a).