Question

Does the table show a direct proportional relationship? If so, what is the constant of proportionality?

Answer 1

C. Yes, 3.5.

Explanation:

If there is a relationship of direct proportionality for every ordered pair of the table, then the constant of proportionality must the same for every ordered pair. The constant of proportionality (
`k`) is described by the following expression:

`k = (y)/(x)` (1)

Where:

`x` - Input.

`y` - Output.

If we know that
`(x_(1), y_(1)) = (13, 45.5)`,
`(x_(2), y_(2)) = (14, 49)` and
`(x_(3), y_(3)) = (15, 52.5)`, then the constants of proportionalities of each ordered pair are, respectively:

`k_(1) = (y_(1))/(x_(1))`

`k_(1) = (45.5)/(13)`

`k_(1) = (7)/(2)`

`k_(2) = (y_2)/(x_2)`

`k_(2) = (49)/(14)`

`k_(2) = (7)/(2)`

`k_(3) = (y_(3))/(x_(3))`

`k_(3) = (52.5)/(15)`

`k_(3) = (7)/(2)`

Since
`k_(1) = k_(2) = k_(3)`, the constant of proportionality is 3.5.