Question

a farm records the average weight of a piglet for the first several weeks of its life. piglet weight

using a linear line - of - best - fit model, approximately what is the predicted weight of a piglet at week 7? 16.3 14.1 17.5 18.6

Explanation:

Step1: Calculate the slope

Let \(x\) be the week and \(y\) be the weight. Using two points \((1,3.1)\) and \((5,12.0)\).
The slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), so \(m=\frac{12.0 - 3.1}{5 - 1}=\frac{8.9}{4}=2.225\)

Step2: Find the equation of the line

Using the point - slope form \(y - y_1=m(x - x_1)\), with \((x_1,y_1)=(1,3.1)\) and \(m = 2.225\)
\(y-3.1=2.225(x - 1)\)
\(y=2.225x-2.225 + 3.1\)
\(y=2.225x+0.875\)

Step3: Predict the weight at week 7

Substitute \(x = 7\) into the equation \(y=2.225\times7+0.875\)
\(y=15.575+0.875=16.45\approx16.3\)

Answer:

16.3