To determine if a relation qualifies as a linear function, we need to check if there is a constant rate of change between the input and output values. This means that for every increase of 1 in the input value, there should be a consistent increase or decrease in the output value.
Let's calculate the rate of change between the given ordered pairs:
From (-5, 7) to (-3, 15), the rate of change is 15 - 7 = 8.
From (-3, 15) to (-1, 23), the rate of change is 23 - 15 = 8.
Since the rate of change is consistent, we can conclude that the relation qualifies as a linear function.
Now, we need to determine which of the given ordered pairs can be placed in the table and still maintain the same rate of change.
The rate of change between (0, 31) and (-1, 23) is 31 - 23 = 8, so (0, 31) can be placed in the table.
The rate of change between (0, 31) and (-5, 7) is 31 - 7 = 24, so (−7, 30) cannot be placed in the table.
The rate of change between (1, 31) and (-1, 23) is 31 - 23 = 8, so (1, 31) can be placed in the table.
The rate of change between (0, 31) and (0, -1) is -1 - 31 = -32, so (0, -1) cannot be placed in the table.
Therefore, the ordered pairs that can be placed in the table and still have the relation qualify as a linear function are:
(0, 31)
(1, 31)
Which of the following ordered pairs could be placed in the table below and still have the relation qualify as a linear function? (4 points)
Input
(x) Output
(y)
−5 7
−3 15
−1 23
? ?
(0, 31)
(−7, 30)
(1, 31)
(0, −1)
1 answer