The forearm length in centimeters, A, can be approximated by a linear function of the foot length in centimeters, f. Use the points (25, 24) and (33, 33) to find a linear model for the data in the table below. $\begin{array}{l|lllllllll}
\text { Foot Length }(\mathrm{cm}) & 29 & 31 & 33 & 26 & 28 & 37 & 25 & 30 & 32 \
\hline \text { Forearm Length }(\mathrm{cm}) & 30 & 30 & 33 & 25 & 28 & 37 & 24 & 31 & 31
\end{array}$

A) $A = f - 1$
B) $\mathrm { A } = 1.125 \mathrm { f } + 4.125$
C) $\mathrm { A } = 1.125 \mathrm { f } - 4.125$
D) $\mathrm { A } = 0.889 \mathrm { f } + 1.775$

Question

The forearm length in centimeters, A, can be approximated by a linear function of the foot length in centimeters, f. Use the points (25, 24) and (33, 33) to find a linear model for the data in the table below. $\begin{array}{l|lllllllll}
\text { Foot Length }(\mathrm{cm}) & 29 & 31 & 33 & 26 & 28 & 37 & 25 & 30 & 32 \
\hline \text { Forearm Length }(\mathrm{cm}) & 30 & 30 & 33 & 25 & 28 & 37 & 24 & 31 & 31
\end{array}$

A) $A = f - 1$
B) $\mathrm { A } = 1.125 \mathrm { f } + 4.125$
C) $\mathrm { A } = 1.125 \mathrm { f } - 4.125$
D) $\mathrm { A } = 0.889 \mathrm { f } + 1.775$

Quizplus · Accepted Answer

To find the linear model, we use the two given points (25, 24) and (33, 33). The slope $m$ of the line is calculated as $\frac{33 - 24}{33 - 25} = \frac{9}{8} = 1.125$. To find the y-intercept $b$, we can use one of the points and the slope in the equation $y = mx + b$. Using the point (25, 24), we get $24 = 1.125(25) + b$, solving for $b$ gives $b = 24 - 1.125(25) = -4.125$. Therefore, the linear model is $A = 1.125f - 4.125$.

The Forearm Length in Centimeters, A, Can Be Approximated by a Linear