The relationship between the quantities in the table is; y = 14·x
A = 56, B = 70, and C = 84
The steps by which the relationship equation and the above values are found can be presented as follows;
The values in the table can be presented as follows;
x y
1 14
2 28
3 42
4 A
5 B
6 C
The ratio of the y-values to the x-values, of the first three ordered pair can be found as follows;
The ratio y/x for the ordered pair (1, 14) is; y/x = 14/1
The ratio y/x for the ordered pair (2, 28) is; 28/2 = 14/1
The ratio y/x for the ordered pair (3, 42) is; 42/3 = 14/1
The ratio is of y/x = 14 for the values in the table, which is a constant, therefore, we get;
y/x = 14
y = 14·x
x = y/14, therefore, the relationship can also be expressed as; x = y/14
When x = 4, we get; y = 4 × 14 = 56
When x = 5, we get; y = 5 × 14 = 70
When x = 6, we get; y = 6 × 14 = 84
The completed table is therefore;
x y
1 14
2 28
3 42
4 56
5 70
6 84
Comparing the above values to the ordered pair (4, A), (5, B), and (6, C), we get;
A = 56, B = 70, and C = 84
The complete question obtained from a similar question found through search can be presented as follows;
A two column table with 6 rows. Column 1 is labeled x with entries 1, 2, 3, 4, 5, 6. Column 2 is labeled y with entries 14, 28, 42, A, B, C. Find the relationship between the quantities in the table. Then use the relationship to calculate the missing values in the table. The relationship between the quantities in the table is x equals y. A = ___, B = ___, C = ___