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
w = 8.9a + 3.6
a = 8.9w + 3.6

Explanation:

Step1: Substitute values

We know that the general form of a linear equation is \(y = mx + b\) (here \(W\) is like \(y\) and \(a\) is like \(x\)). Let's substitute the values from the table. For example, when \(a = 2\), \(W=16\); when \(a = 3\), \(W = 20\).
For the equation \(W=3.6a + 8.9\), when \(a = 2\), \(W=3.6\times2+8.9=7.2 + 8.9=16.1\approx16\). When \(a = 3\), \(W=3.6\times3+8.9 = 10.8+8.9=19.7\approx20\).
For the equation \(W = 8.9a+3.6\), when \(a = 2\), \(W=8.9\times2+3.6=17.8 + 3.6=21.4
eq16\).
The equation \(W = 3.6+8.9\) is not a linear equation in terms of \(a\) (it's a constant). The equation \(a=8.9W + 3.6\) is solving for \(a\) in terms of \(W\), but we need \(W\) in terms of \(a\) as per the relationship of weight (\(W\)) depending on age (\(a\)).

Answer:

\(W = 3.6a+8.9\)