Which table of values represents a linear function?
A
xx yy
minus, 3−3 00
minus, 1−1 11
33 33
55 44
B
xx yy
minus, 4−4 00
minus, 3−3 22
minus, 1−1 44
11 66
C
xx yy
minus, 7−7 33
minus, 2−2 00
33 minus, 3−3
88 minus, 7−7
D
xx yy
minus, 6−6 44
minus, 4−4 33
minus, 1−1 11
11 00
The table of values that represents a linear function is table A.
This is because in a linear function, the change in y is directly proportional to the change in x. In table A, as x increases by 2, y increases by 1. And as x decreases by 2, y decreases by 1. This shows a constant rate of change and is characteristic of a linear function.
The table of values that represents a linear function is B.
In option B, the values of y increase by 2 for each increase of 1 in x, indicating a constant rate of change. This is a characteristic of a linear function.
To determine which table of values represents a linear function, we need to check if the difference between the y-values (denoted as 'yy') is constant for each pair of x-values (denoted as 'xx').
Let's examine each table:
Table A:
xx yy
-3 0
-1 1
3 3
5 4
By comparing the differences between consecutive y-values, we can see that the values are not constant. For example, the difference between the first pair of y-values (-3 and 0) is 3, while the difference between the second pair (0 and 1) is only 1. Therefore, Table A does not represent a linear function.
Table B:
xx yy
-4 0
-3 2
-1 4
1 6
By comparing the differences between consecutive y-values in this table, we can see that the differences are constant. The difference between each pair of y-values is always 2. Therefore, Table B represents a linear function.
Table C:
xx yy
-7 3
-2 0
3 -3
8 -7
By comparing the differences between consecutive y-values, we can see that the values are not constant. For example, the difference between the first pair of y-values (3 and 0) is 3, but the difference between the second pair (0 and -3) is 3 as well. Therefore, Table C does not represent a linear function.
Table D:
xx yy
-6 4
-4 3
-1 1
1 0
By comparing the differences between consecutive y-values in this table, we can see that the differences are constant. The difference between each pair of y-values is always -1. Therefore, Table D represents a linear function.
In conclusion, the table that represents a linear function is Table B.