the scatterplot above shows the number of visitors to a railroad museum in pennsylvania each year from 1968…

Explanation:

Step1: Identify the form of a linear - regression line

The equation of a line is in the form (y = mx + b), where (m) is the slope and (b) is the y - intercept. In the context of the scatter - plot, if (y) is the number of visitors (n) and (x) is the number of years since 1968 ((t)), the equation is (n=mt + b).

Step2: Determine the slope and y - intercept from the scatter - plot

The line is decreasing, so the slope (m) is negative. When (t = 0) (the year 1968), the y - intercept (b) is the number of visitors in 1968. Looking at the scatter - plot, as (t) increases, (n) decreases. A possible equation could be of the form (n=-at + b) where (a>0). For example, if we assume two points on the line of best - fit ((t_1,n_1)) and ((t_2,n_2)), the slope (m=\frac{n_2 - n_1}{t_2 - t_1}<0).

Since no specific points or options are given, a general form of a line of best - fit for a decreasing linear relationship between the number of years since 1968 ((t)) and the number of visitors (n) is (n=-kt + c), where (k>0) is the slope (representing the rate of decrease of visitors per year) and (c) is the number of visitors in 1968 (the y - intercept when (t = 0)).

Answer:

A general form of the line of best - fit is (n=-kt + c) ((k>0), (c) is the number of visitors in 1968)