Question

A Nielsen survey of 3000 American moviegoers aged 12−74 found that 27% of them used social media to chat about movies in 2010. The percentage was 29% in 2011 and 31% in 2012. Let t=0,t=1, and t=2 correspond to the years 2010, 2011, and 2012, respectively, 1 (a) Explain why the three points P

1
​
(0,27),P
2
​
(1,29), and P
3
​
(2,31) lie on a straight line L. The slope of the line passing through P
1
​
(0,27) and P
2
​
(1,29) is m
1
​
, which is equal to the slope of the line through P
2
​
(1,29) and P
3
​
(2,31), which is m
2
​
= Thus, the three points lie on the line L. (b) If the trend continues, what will the percentage of moviegoers who use social media to chat about movis be in 2018 ? (c) Find an equation of L. (Let t be the independent variable and L be the dependent variable.) L=

Answer 1

(a) The three points P1(0,27), P2(1,29), and P3(2,31) lie on a straight line L because the slope between any two points is the same. The slope between P1 and P2 (m1) can be calculated as (29-27)/(1-0) = 2/1 = 2. Similarly, the slope between P2 and P3 (m2) is (31-29)/(2-1) = 2/1 = 2. Since the slopes are equal, the points lie on the same line.

(b) To predict the percentage of moviegoers who use social media to chat about movies in 2018, we can extend the trend line. We can assume that the trend continues with a constant slope of 2. Considering 2018 as t = 8 (since it is 8 years after 2010), we can calculate the y-value using the equation of the line.

L = mt + c

L = 28 + c (where c is the y-intercept)

To find the y-intercept (c), we can use any of the given points. Let's use P1(0,27):

27 = 2*0 + c

c = 27

Now, we can substitute the values back into the equation:

L = 2*t + 27

Therefore, the percentage of moviegoers who use social media to chat about movies in 2018 is L = 2*8 + 27 = 16 + 27 = 43%.

(c) The equation of the line L is L = 2*t + 27.