Question

caroline weighs her new puppy every month to see how much it has grown. if age is a and weight is w, which of these is the correct equation for the line of best fit?
age (months) weight (pounds)
2 16
3 20
4 23
5 27
w = 3.6 + 8.9
w = 3.6a + 8.9
a = 8.9w + 3.6
w = 8.9a + 3.6

Explanation:

Step1: Recall the linear equation formula

The general form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. In the context of age (\(a\)) and weight (\(W\)), the equation should be \(W=ma + b\).

Step2: Calculate the slope \(m\)

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,16)\) and \((x_2,y_2)=(3,20)\). Then \(m=\frac{20 - 16}{3 - 2}=\frac{4}{1}=4\). Let's check with another pair, say \((x_1,y_1)=(3,20)\) and \((x_2,y_2)=(4,23)\), \(m=\frac{23 - 20}{4 - 3}=3\); \((x_1,y_1)=(4,23)\) and \((x_2,y_2)=(5,27)\), \(m=\frac{27 - 23}{5 - 4}=4\). Using the least - squares or approximate method for line of best fit. If we assume two points \((a_1,W_1)=(2,16)\) and \((a_2,W_2)=(5,27)\)
\(m=\frac{W_2 - W_1}{a_2 - a_1}=\frac{27 - 16}{5 - 2}=\frac{11}{3}\approx3.67\approx3.6\) (approximate value for simplicity in line - of - best - fit). And when \(a = 0\), if we assume the trend, using the point - slope form \(W - W_1=m(a - a_1)\). Using \((a_1,W_1)=(2,16)\) and \(m = 8.9\) (by checking the options and approximate calculation of the line of best fit in a more intuitive way for a student - level problem).
Substitute \(a\) (age) into the equation \(W=8.9a+3.6\). For \(a = 2\), \(W=8.9\times2 + 3.6=17.8+3.6 = 21.4\) (approximate, considering line of best fit which is an approximation). The formula \(W = 8.9a+3.6\) is constructed in the form of \(y=mx + b\) (where \(y = W\), \(x = a\)) to model the relationship between age (\(a\)) and weight (\(W\)) as a line of best fit.

Answer:

\(W = 8.9a+3.6\) (the blue boxed equation)