Write an equation of the trend line, rounding to two decimal places as needed. For this problem, choose the points (1990, 252) and (2002, 325). Choose the correct answer below.
The equation of the trend line can be found using the formula:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are the coordinates of the two points on the line.
In this case, the coordinates are (1990, 252) and (2002, 325).
m = (325 - 252) / (2002 - 1990)
= 73 / 12
= 6.08 (rounded to two decimal places)
Now we can use one of the points and the slope to find the equation of the line. Let's use the first point (1990, 252).
y - 252 = 6.08(x - 1990)
Simplifying:
y - 252 = 6.08x - 12115.2
y = 6.08x - 12115.2 + 252
y = 6.08x - 11863.2
Therefore, the equation of the trend line is y = 6.08x - 11863.2.
Estimate the attendance at theme parks in the country in 2005.
The estimated attendance was ____ million.
(Round to the nearest whole number as needed. Use the answer from the previous part to find this answer.)
To estimate the attendance at theme parks in the country in 2005, we can substitute the year 2005 into the equation of the trend line we found earlier.
y = 6.08x - 11863.2
Substituting x=2005 into the equation:
y = 6.08(2005) - 11863.2
y ≈ 12170 - 11863.2
y ≈ 306.8
Rounding to the nearest whole number, the estimated attendance at theme parks in the country in 2005 is 307 million.
To find the equation of the trend line, you can use the slope-intercept form of a linear equation, which is given by y = mx + b.
First, calculate the slope (m) of the trend line using the formula:
m = (y2 - y1) / (x2 - x1)
Given points:
Point 1: (1990, 252)
Point 2: (2002, 325)
Substituting the values into the formula:
m = (325 - 252) / (2002 - 1990)
m = 73 / 12
Next, substitute the value of the slope (m) and any one of the given points (x, y) into the slope-intercept form equation:
y = mx + b
Using point (1990, 252):
252 = (73/12) * 1990 + b
Now, solve for b:
b = 252 - (73/12) * 1990
To find the equation of the trend line, substitute the values of m and b into the equation:
y = (73/12)x + (252 - (73/12) * 1990)
Simplifying the equation and rounding to two decimal places, the trend line equation is:
y = (6.08)x + 44.83
Therefore, the equation of the trend line, rounded to two decimal places, is y = 6.08x + 44.83.