Question

1. a linear model for the data:

(a) which two points should you use to find the equation of the model? explain
(b) use the two points you chose in part (a) to find the slope of the linear model rounded to three decimal places. show your work

Explanation:

Step1: Select points for accuracy

To find the equation of a linear model, we should choose two points that lie on or close to the line of best - fit. Looking at the scatter - plot, the points (1, 14) and (7, 7) seem to be good choices as they are on or near the trend line.

Step2: Calculate the slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 1,y_1=14,x_2 = 7,y_2 = 7$.
\[m=\frac{7 - 14}{7 - 1}=\frac{-7}{6}\approx - 1.17\]

Answer:

(a) The points (1, 14) and (7, 7) should be used. They are on or near the line of best - fit for the data points in the scatter - plot.
(b) The slope of the linear model is approximately $-1.17$.