The table below shows the attendance in millions at theme parks in a certain country. Make a scatter plot of the data pairs. Draw a trend line and write its equation. Estimate the attendance at theme parks in the country in 2005.
Year
1990
1992
1994
1996
1998
2000
2002
2004
2006
Attendance (millions)
251
268
266
293
301
320
322
327
335
Let x be the year and let y be the attendance that year in millions. Make a scatter plot of the data pairs and draw a trend line. Choose the correct graph below.
d
Write an equation of the trend line, rounding to two decimal places as needed. For this problem, choose the points (1990,251) and (2022,322)
Choose the correct answer below.
A. y=5.92x-11,523.17
B. y=-5.92x-504.92
C. y=-5.92x+11,523.17
D. y=5.92x+504.92
The correct scatter plot is d.
To find the equation of the trend line, we can use the formula for a linear equation:
y = mx + b
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (1990,251) and (2022,322), we have:
m = (322 - 251) / (2022 - 1990)
m = 71 / 32
m ≈ 2.22
Now we can substitute the slope into the equation formula and one of the points to find the y-intercept (b).
Using (1990,251):
251 = 2.22(1990) + b
251 = 4423.8 + b
b ≈ -4172.8
So the equation of the trend line is:
y = 2.22x - 4172.8
Rounding to two decimal places, the equation is:
y = 2.22x - 4172.80
Now we can estimate the attendance at theme parks in the country in 2005 by plugging in x = 2005 into the equation:
y = 2.22(2005) - 4172.80
y ≈ 322.10
Therefore, the estimated attendance at theme parks in the country in 2005 is approximately 322.10 million.