Question

the scatterplot above shows the number of visitors to a railroad museum in pennsylvania each year from 1968 to 1980, where t is the number of years since 1968 and n is the number of visitors. a line of best fit is also shown. which of the following could be an equation of the line of best fit shown?

Explanation:

Step1: Identify the form of a linear - equation

The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the context of the problem, let $y$ be the number of visitors and $t$ be the number of years since 1968.

Step2: Determine the slope

The slope $m$ can be estimated by looking at the change in $y$ (number of visitors) over the change in $t$ (years). The line is decreasing, so the slope is negative. If we take two points on the line, say $(t_1,y_1)$ and $(t_2,y_2)$, the slope $m=\frac{y_2 - y_1}{t_2 - t_1}$. As the number of visitors is decreasing over the years, and the initial number of visitors (when $t = 0$) is around 20000, and it is decreasing by a certain amount each year.

Step3: Determine the y - intercept

The y - intercept $b$ is the value of $y$ when $t = 0$. From the graph, when $t=0$ (in 1968), the number of visitors is around 20000. So $b\approx20000$.
A possible equation of the line of best fit could be of the form $n=-2000t + 20000$ (assuming the number of visitors $n$ and $t$ is years since 1968), where the slope of - 2000 means the number of visitors is decreasing by 2000 each year and the y - intercept of 20000 is the initial number of visitors in 1968.

Answer:

A possible equation is $n=-2000t + 20000$ (where $n$ is the number of visitors and $t$ is the number of years since 1968)