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

Yes, "y" varies directly with "x"

The constant of variation is:

Step-by-step explanation:

Constant variation equation has the following form:

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   and solve for "k". Then:

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

Step-by-step 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.

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