If x varies directly as y and x=9 when y=2 find x when y is 6

the x = kx

when x=9 , then y=2

9 = 2k
k = 9/2

when y=6
x=x(9/2)(6) = 27

or, by simple ratio:
x/9 = 6/2 = 3
x = 9(3) = 27

noticed a silly typo in 4th-last line

should say:

x= (9/2)(6) = 27

To find the value of x when y is 6, we can use the concept of direct variation. Direct variation represents a relationship between two variables where one variable increases or decreases in proportion to the other variable.

In this case, we have x varying directly as y, which can be expressed as:

x = ky

Where k is the constant of variation.

To find the value of k, we can use the given information: x = 9 when y = 2. Plugging these values into the equation, we get:

9 = k * 2

To solve for k, divide both sides of the equation by 2:

k = 9 / 2

k = 4.5

Now that we have the value of k, we can substitute it back into the original equation and solve for x when y = 6:

x = 4.5 * 6

x = 27

Therefore, when y is 6, x equals 27.