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

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 ratios for the given values:

For x = 4, y = 6.4; y/x = 6.4/4 = 1.6
For x = 7, y = 11.2; y/x = 11.2/7 = 1.6
For x = 10, y = 16; y/x = 16/10 = 1.6
For x = 13, y = 20.8; y/x = 20.8/13 ≈ 1.6

Since the ratio of y to x is the same for all values, we can conclude that y varies directly with x.

The constant of variation, k, can be found by calculating the ratio of y to x for any of the given values. Let's use the first pair, x = 4 and y = 6.4:

k = y/x = 6.4/4 = 1.6

The equation expressing the direct variation in this case is:
y = kx

Substituting k = 1.6, the equation becomes:
y = 1.6x