Question

Suppose that Y varies directly with X, and Y= 4 when X=16

(a) Write a direct variation equation that relates X and Y
(b) Find Y when X = 3

Answer 1

The direct variation equation relating X and Y is Y = 0.25X. To find Y when X = 3, substitute 3 into the equation to get Y = 0.75.

Step-by-step explanation:

When we say that Y varies directly with X, it means that the ratio of Y to X is constant. Given that Y = 4 when X = 16, we can find the constant of variation k by dividing Y by X. Thus, k = Y / X = 4 / 16 = 0.25. This gives us the direct variation equation Y = kX.

Using the constant k, the equation becomes Y = 0.25X.

To find Y when X = 3, substitute X with 3 in the equation Y = 0.25X, which gives Y = 0.25(3) = 0.75.