Question

Determine whether y varies directly with x. If so, find the constant of variable k.

X. Y
6. 24
18. 72
54. 216
162. 648

Answer 1

y varies directly with x, and the constant of variation is k = 4.

Explanation:

If y varies directly with x, then y = kx, where k is the constant of variation.

To determine if y varies directly with x, divide each y value by the corresponding x value. If the result is the same for all the points, then y indeed varies directly with x.

24 / 6 = 4

72 / 18 = 4

216 / 54 = 4

648 / 162 = 4

y varies directly with x, and the constant of variation is k = 4.

Answer 2

Yes, "y" varies directly with "x"

The constant of variation is:
`k=4`

Explanation:

Constant variation equation has the following form:

`y=kx`

Where "k" is the constant of variation.

You can notice in the table the when "x" increases, "y" increases and the ratio between them is always the same.

To find "k" you need to pick any a point from the table, subsitutte the coordinates into
`y=kx` and solve for "k". Then:

`24=k(6)\\\\k=(24)/(6)\\\\k=4`