Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear.
-$$\begin{array} { l | l l l l l l l l l }
\text { Foot Length } ( \mathrm { cm } ) & 25 & 26 & 28 & 29 & 30 & 31 & 32 & 33 & 37 \
\hline \text { Forearm Length } ( \mathrm { cm } ) & 24 & 25 & 28 & 30 & 31 & 30 & 31 & 33 & 37
\end{array}$$
A) exactly linear
B) nonlinear
C) approximately linear

Question

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear.
-$$\begin{array} { l | l l l l l l l l l } 
\text { Foot Length } ( \mathrm { cm } ) & 25 & 26 & 28 & 29 & 30 & 31 & 32 & 33 & 37 \
\hline \text { Forearm Length } ( \mathrm { cm } ) & 24 & 25 & 28 & 30 & 31 & 30 & 31 & 33 & 37
\end{array}$$
A) exactly linear
B) nonlinear
C) approximately linear

Quizplus · Accepted Answer

To determine if the data set is linear, we can look at the rate of change between points. In this case, as the foot length increases, the forearm length also increases, but not at a constant rate. For example, from 25 cm to 26 cm foot length, the forearm length increases by 1 cm, but from 30 cm to 31 cm foot length, the forearm length decreases by 1 cm before increasing again. This indicates the relationship is not exactly linear but does show a general trend of increase, suggesting it is approximately linear rather than nonlinear.

Without Graphing, Determine Whether the Following Data Set Is Exactly