Question

the puppy was weighed again at 9 months old and weighed 52 pounds. data set b consists of all the data points in data set a as well as the data point (9, 52). the equation of a line of best fit for data set b can be written as y = r + sx, where r and s are constants and 2 ≤ x ≤ 9. assuming the equations of the lines of best fit are calculated in the same way, which of the following is the best estimate for the value of s? a 5.9 b 8.7 c 13.8 d 17.7

Explanation:

Step1: Recall slope formula

The equation of a line is $y = r+ sx$, where $s$ is the slope. The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $s=\frac{y_2 - y_1}{x_2 - x_1}$. We can use two - point approximation for the line of best - fit. Let's assume we use the first visible point (around $(2,12)$) and the new point $(9,52)$.

Step2: Substitute points into slope formula

Here, $x_1 = 2,y_1=12,x_2 = 9,y_2 = 52$. Then $s=\frac{52 - 12}{9 - 2}=\frac{40}{7}\approx5.71$. Among the given options, the closest value to our approximation is 5.9.

Answer:

A. 5.9