X Y

Question

4 6.4
7 11.2
10 16
13 20.8
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.

Answer 1

To determine whether y varies directly with x, we need to check if the ratio of y to x is constant for all values.

Let's calculate the ratio of y to x for each pair:

For the first pair (4, 6.4):

ratio = 6.4/4 = 1.6

For the second pair (7, 11.2):

ratio = 11.2/7 = 1.6 (same as the first pair)

For the third pair (10, 16):

ratio = 16/10 = 1.6 (same as the previous pairs)

For the fourth pair (13, 20.8):

ratio = 20.8/13 = 1.6 (same as the previous pairs)

Since the ratio of y to x is constant (1.6) for all pairs, we can conclude that y varies directly with x.

To find the constant of variation (k), we can select any pair of x and y and use the formula:

k = y / x

Let's choose the first pair (4, 6.4):

k = 6.4 / 4 = 1.6

Therefore, the constant of variation is k = 1.6.

The equation for the direct variation is:

y = kx

Substituting the value of k, we get:

y = 1.6x