Which table represents a linear function?
x y
0 1
1 3
2 -3
3 -1
x y
0 0
1 1
2 4
3 9
x y
0 0
1 -1
2 4
3 -9
x y
0 3
1 1
2 -1
3 -3
Question & Answer
Which table represents a linear function?
1 Answer
Verified archiveTo determine which table represents a linear function, we need to check if the relationship between ( x ) and ( y ) is consistent and has a constant rate of change (slope).
1. Table 1:
– ( (0, 1), (1, 3), (2, -3), (3, -1) )
– The changes in ( y ) are not constant: ( 2, -6, +2 ) (not linear).
2. Table 2:
– ( (0, 0), (1, 1), (2, 4), (3, 9) )
– The changes in ( y ) are: ( 1, 3, 5 ) (not linear).
3. Table 3:
– ( (0, 0), (1, -1), (2, 4), (3, -9) )
– The changes in ( y ) are inconsistent: ( -1, 5, -13 ) (not linear).
4. Table 4:
– ( (0, 3), (1, 1), (2, -1), (3, -3) )
– The changes in ( y ) are: ( -2, -2, -2 ) (constant slope of -2, which is linear