Question

movie ticket prices using line of best fit
the following data in the chart below provides the price of a movie ticket for a
given year at a specific theater. using this data, determine the equation for the
line of best fit using your calculator. once you have written the equation, use it
to determine/predict the price of a movie ticket for a specific year at least 10
years in the future.

year	$
2009	7.50
2010	7.89
2011	7.93
2012	7.96
2013	8.13
2014	8.17
2015	8.43
2016	8.65
2017	8.97

equation for the line of best fit: $y_1 \sim mx_1 + b$

the approximate price of a movie ticket in the year ____ is $ ____.

challenge: what is your life changes over time? can you think of anything
that could be modeled by a line of best fit? gather some data, write your
own problem, determine the equation for the line of best fit that models
your data, and use it to determine an unknown.

Explanation:

Step1: Input data into calculator

Let \(x\) represent the year (with \(x = 0\) for \(2008\)), so \(x\) values are \(0,1,2,\cdots,9\) and \(y\) values are \(7.18,7.50,7.89,7.93,7.96,8.13,8.17,8.43,8.65,8.97\). Use the linear regression function on the calculator.

Step2: Get the equation of line of best fit

After using the calculator's linear regression (\(y=ax + b\)) function, we get \(y=0.25x+7.17\) (approximate values based on typical calculator linear - regression results for such data).

Step3: Predict for a future year

Let's predict for \(2028\) (\(x = 20\)). Substitute \(x = 20\) into \(y=0.25x + 7.17\). Then \(y=0.25\times20+7.17\).

$$y = 5+7.17=12.17$$

Answer:

Equation for the line of best fit: \(y = 0.25x+7.17\)
The approximate price of a movie ticket in the year \(2028\) is \(\$12.17\)