The function rule for the linear function is y = y = x - 12
The missing values are: x = 6; and y = -22.
What is a Linear Function Rule?
Where, m is the average rate of change, and b is the initial value when x is 0, therefore, a linear function rule is given as, y = mx + b.
Find m and b using the table of values given.
Using (32, 20) and (14, 2):
Average rate of change (m) = change in y / change in x = (20 - 2)/(32 - 14)
Average rate of change (m) = 18/18 = 1.
Find b by substituting m = 1 and (x, y) = (14, 2) into y = mx + b
2 = 1(14) + b
2 = 14 + b
2 - 14 + b
-12 = b
b = -12
Write the rule of the linear function by substituting m = 1 and b = -12 into y = mx + b
y = 1(x) + (-12)
y = x - 12
Find the missing values on the table
Fourth Row: when y = -6
-6 = x - 12
-6 + 12 = x
x = 6
Last Row: when x = -10
y = -10 - 12
y = -22
Therefore, the function rule for the linear function is y = y = x - 12
The missing values are: x = 6; and y = -22.
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