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.