Final answer:
The equation describing the relationship between the number of cinema sites and years past 2000 is y = -220x + 6700. To predict the number of cinema sites in 2009, substitute x = 9 into the equation, resulting in a predicted value of 4720.
Step-by-step explanation:
To write an equation describing the relationship between the number of cinema sites and years past 2000, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this case, y represents the number of cinema sites and x represents the years past 2000.
The slope (m) can be found using the formula (change in y)/(change in x), and the y-intercept (b) can be found by substituting one set of ordered pairs into the equation.
From 2000 to 2004, the change in years past 2000 is 4, and the change in the number of cinema sites is -880. Therefore, the slope (m) is -880/4 = -220.
We can substitute the ordered pair (0, 6700) into the equation to find the y-intercept (b).
So, the equation describing the relationship is y = -220x + 6700, where y is the number of cinema sites and x is the years past 2000.
To predict the number of cinema sites in 2009, we substitute x = 9 (since 2009 is 9 years past 2000) into the equation:
y = -220(9) + 6700
y = -1980 + 6700
y = 4720.
Therefore, the predicted number of cinema sites in 2009 is 4720.