Final answer:
In a direct variation scenario with y = 90 when x = 10, we determined the constant of variation (k) to be 9. Using the derived equation y = 9x, we found that when y is 18, x equals 2.
Step-by-step explanation:
The student's question is focused on understanding direct variation in a mathematical relationship between two variables, x and y. In this scenario, we are given that y varies directly as x, and when y is 90, x is 10. We use this information to derive the direct variation equation y = kx, where k is the constant of variation. Let's find the value of k using the given values.
90 = k(10)
k = 90 / 10 = 9
Now that we have determined the constant of variation is 9, the equation can be written as y = 9x. To find the value of x when y is 18, we substitute 18 for y in the equation and solve for x:
18 = 9x
x = 18 / 9
x = 2
So, when y is 18, x is 2.