Question

If y varies directly as x, and y = 2 when x = 3, find the constant of variation for the relation and use it to write an equation for the statement. Then solve the equation.

A) The constant of variation is 2, and the equation is y = 2x. When x = 1, y = 2.
B) The constant of variation is 3, and the equation is y = 3x. When x = 1, y = 3.
C) The constant of variation is 1/2, and the equation is y = (1/2)x. When x = 1, y = 1/2.
D) The constant of variation is 6, and the equation is y = 6x. When x = 1, y = 6.

Answer 1

The constant of variation is 2/3, making the equation y = (2/3)x. When x = 1, y equals 2/3.

Step-by-step explanation:

When variables such as x and y are directly proportional, there is a constant of variation, typically represented as k, that relates them in the equation y = kx. Given that y equals 2 when x equals 3, we can determine the constant of variation by substituting these values into the equation to solve for k:

k = y / x = 2 / 3

Hence, the constant of variation is 2/3, and the equation that represents this direct relationship is y = (2/3)x. To solve for y when x = 1, we substitute 1 into the equation:

y = (2/3)(1) = 2/3

Therefore, when x = 1, y equals 2/3.