A linear model is given for the data in the table: y=10x+1
X y
1 9
2 21
3 29
4 41
5 49
6 61
7 69
A) 8
B) -8
C) -16
D) 16
The slope of the linear model y=10x+1 is 10, so the difference in y-values between any two points is 10 times the difference in their corresponding x-values. Looking at the table, we see that the difference in x-values between 6 and 2 is 4, so the difference in y-values between those two points should be 4 times 10, which is 40.
Starting from y=21 at x=2, if we go down 40 units (because we want the difference in y-values to be negative), we get y=-19. Therefore, the answer is B) -8, because 2-(-6) = 8.
To determine the missing value in the table using the given linear model y = 10x + 1, we need to substitute the given value for x into the equation and solve for y.
Let's consider the options one by one:
A) 8:
Substituting x = 8 into the equation, we get y = 10(8) + 1 = 81. However, 81 is not in the given table.
B) -8:
Substituting x = -8 into the equation, we get y = 10(-8) + 1 = -79. However, -79 is not in the given table.
C) -16:
Substituting x = -16 into the equation, we get y = 10(-16) + 1 = -159. However, -159 is not in the given table.
D) 16:
Substituting x = 16 into the equation, we get y = 10(16) + 1 = 161. However, 161 is not in the given table.
Since none of the given options match any of the values in the table, we cannot determine the missing value using the given linear model.