determine whether y varies directly with x if so find the constant of variation k and write the equation.

Question

X Y
6 24
18 72
54 216
162 648

Answer 1

To determine if y varies directly with x, we can check if the ratio between y and x stays constant.

Let's calculate the ratio between y and x for each pair of values:

For the first pair (x = 6, y = 24), the ratio is 24/6 = 4.
For the second pair (x = 18, y = 72), the ratio is 72/18 = 4.
For the third pair (x = 54, y = 216), the ratio is 216/54 = 4.
For the fourth pair (x = 162, y = 648), the ratio is 648/162 = 4.

Since the ratio between y and x is constant (4), we can conclude that y varies directly with x.

The constant of variation (k) is then equal to this ratio, which is 4.

The equation that relates y and x is given by y = kx. In this case, the equation is y = 4x.