Question

If x varies directly with y and x = -3 when y = 12, what is the constant of variation?

Answer 1

The constant of variation is -1/4, calculated by substituting the given values of x and y into the direct variation equation x = ky.

Step-by-step explanation:

If x varies directly with y, this means that x can be expressed as a product of y and a constant of variation k (x = ky). When x = -3 and y = 12, we can substitute these values into the direct variation equation to find k:

x = ky

-3 = k(12)

-3/12 = k

k = -1/4

Therefore, the constant of variation is -1/4.

Answer 2

k = -
`(1)/(4)`

Step-by-step explanation:

Given that x varies directly with y then the equation relating them is

x = ky ← k is the constant of variation

To find k use the condition x = - 3 when y = 12

- 3 = 12k ( divide both sides by 12 )

`(-3)/(12)` = k , that is

k = -
`(1)/(4)`