Final answer:
To determine which additional ordered pairs can be added to the given set and still represent the same linear function, we need to find the slope of the function and compare it with the given options. By equating the slopes, we can find the missing values and identify the correct pairs. Option c) (2, -2) and (5, -11) can be added to the given set and still represent the same linear function.
Step-by-step explanation:
In this question, we are given a set of ordered pairs that model a linear function rule. To determine which two ordered pairs can be added to the given set and still represent the same linear function, we need to find the slope of the function and see which pairs have the same slope as the given set.
To find the slope, we can use the formula:
slope = (change in y)/(change in x)
Using the first two ordered pairs, (-2, 10) and (-1.7, ?), we have:
slope = (10 - ?)/(-2 - (-1.7)) = (10 - ?)/(-0.3)
Using the second and third ordered pairs, (-1.7, ?) and (0.4, ?), we have:
slope = (?, ?)/(-1.7 - 0.4) = (?, ?)/(-2.1)
Using the third and fourth ordered pairs, (0.4, ?) and (1, 1), we have:
slope = (1 - ?)/(1 - 0.4) = (1 - ?)/0.6
By equating the above expressions for slope, we can find the missing values. Based on the given options, it can be seen that the pair of ordered pairs (2, -2) and (5, -11) will have the same slope as the given set. Therefore, option c) (2, -2) and (5, -11) can be added to the given set and still represent the same linear function.