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To find the linear model for this relationship, we can use the two data points given to create a system of equations and then solve for the slope and y-intercept.
Let's call the time spent on social media T and the age a. Using the two observations provided:
1) When a = 50, T = 8
8 = 50m + b
2) When a = 20, T = 20
20 = 20m + b
Now we can solve this system of equations to find the values of m (slope) and b (y-intercept).
From the second equation, we get:
20 = 20m + b
b = 20 - 20m
Substitute this into the first equation:
8 = 50m + (20 - 20m)
8 = 30m + 20
30m = -12
m = -12/30
m = -0.4
Now substitute m back into the second equation to find b:
20 = 20(-0.4) + b
20 = -8 + b
b = 28
Therefore, the linear model for the relationship between time spent on social media T (in hr) and age a (in yr) is:
T = -0.4a + 28