Question

The value of y is directly proportional to x, and y, equals, 6y=6 when x, equals, 18x=18. determine a function that represents the relationship and find x when y, equals, 4y=4

Answer 1

Given that y is directly proportional to x with y = 6 when x = 18, we find the proportionality constant k = 1/3. The function representing the relationship is y = (1/3)x. We solve for x when y = 4, getting x = 12.

Step-by-step explanation:

To solve the mathematical problem completely regarding the direct proportionality of two variables, we must first determine the proportionality constant. Given that y is directly proportional to x and that for a value of x = 18, y = 6, we can set up the equation as y = kx. To find the constant of proportionality k, we use the provided values:

y = kx
6 = k × 18

Solving for k gives us:

k = 6 / 18
k = 1/3

With k determined, our function that represents the relationship between x and y is:

y = (1/3)x

Now we can find the value of x when y is 4:

4 = (1/3)x
x = 4 / (1/3)
x = 4 × 3
x = 12

Therefore, the value of x when y equals 4 is 12.