The missing values are x = 8 and y = 20. This determination aligns with the linear relationship exhibited in the given dataset, affirming the correctness of Missing x: 8, Missing y: 20. Here option A is correct.
To determine the missing data values, the rate of change between the provided x and y values needs to be calculated, representing the slope of the linear function.
The rate of change (slope) is found by taking the difference in y-values and dividing it by the difference in x-values. Using the first two data pairs (4, 17) and (6, 19), the rate of change is determined as (19 - 17) / (6 - 4) = 2 / 2 = 1. This implies that for every unit increase in x, y increases by 1 unit.
Applying this rate of change to the third row, where y is 21, subtracting 1 yields the missing x-value: 21 - 1 = 20. Similarly, for the fourth row with x as 10, adding 1 gives the missing y-value: 10 + 1 = 11. Thus, the missing data values are x = 8 and y = 20, and the correct answer is a. Missing x: 8, Missing y: 20.