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Input (x) Output (y)
32 20
14 2
?
−
6
-
6
−
2
-
2
−
14
-
14
−
10
-
10
?
Complete the function table and write the function rule.
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To complete the function table, we need to find the corresponding output for the input missing input value:
Input (x) Output (y)
32 20
14 2
-6 -6
-2 -2
-14 -10
-10 ?
To find the output for the input value of -10, we can assume that there is a linear relationship between the inputs and outputs and use the two known data points (32,20) and (14,2) to find the slope of the line and then use that slope to find the output for the missing input value.
Slope = (change in y)/(change in x) = (20-2)/(32-14) = 18/18 = 1
Using the slope and one of the known data points, we can find the y-intercept (b) of the line:
y = mx + b
2 = 1(14) + b
b = -12
So the function rule is:
y = x - 12
Therefore, the missing output for the input value of -10 is:
y = -10 - 12 = -22