Write an equation of the trend line, rounding to two decimal places as needed. For this problem, choose the points (1990,255) and (2002,321). Choose the correct answer below.
A. y = -5.5x - 587.5
B. y = 5.5x + 587.5
C. y = -5.5x + 10,690
D. y = 5.5x - 10,690
To find the equation of the trend line, we can use the equation of a line:
y = mx + b
where m is the slope and b is the y-intercept.
First, let's find the slope. The slope (m) is given by:
m = (y2 - y1) / (x2 - x1)
Using the points (1990, 255) and (2002, 321), we have:
m = (321 - 255) / (2002 - 1990)
m = 66 / 12
m = 5.5
Now, we can find the y-intercept by substituting the slope (m) and one of the points into the equation:
255 = 5.5(1990) + b
255 = 10,945 + b
To solve for b, we subtract 10,945 from both sides:
255 - 10,945 = b
b = -10,690
Therefore, the equation of the trend line is:
y = 5.5x - 10,690
The correct answer is D. y = 5.5x - 10,690.
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 use the equation of the trend line and substitute x=2005 into it.
The equation of the trend line is:
y = 5.5x - 10,690
Substituting x=2005 into the equation, we have:
y = 5.5(2005) - 10,690
y = 11,027.5 - 10,690
y ≈ 337.5
Rounding to the nearest whole number, the estimated attendance at theme parks in the country in 2005 is 338 million.
Therefore, the answer is 338.
To find the equation of the trend line, we can use the formula for the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
First, let's calculate the slope (m) using the two given points (1990, 255) and (2002, 321).
The slope (m) can be found using the formula: m = (y2 - y1) / (x2 - x1)
Substituting the values, we get: m = (321 - 255) / (2002 - 1990)
Simplifying, we have: m = 66 / 12
Calculating further, we find: m = 5.5
Next, we need to find the y-intercept (b) by substituting one of the points and the calculated slope (m) into the equation y = mx + b.
Using the point (1990, 255), we have: 255 = 5.5(1990) + b
Simplifying, we have: 255 = 10,945 + b
Solving for b: b = 255 - 10,945
Calculating further, we find: b = -10,690
Therefore, the equation of the trend line is: y = 5.5x - 10,690
The correct answer is D. y = 5.5x - 10,690.