if y varies directly as x,and x=9 and when y=15'find y when x=33

y2:x2=y1:x1

so
y2=(y1/x1)*x2
=(15/9)*33

To find the value of y when x is 33 in a direct variation relationship, we can use the concept of proportional relationships. In a direct variation, y varies directly as x, which can be represented by the equation y = kx, where k is the constant of variation.

To determine the value of k, we can use the given information that when x is 9, y is 15. Substituting these values into the equation, we get:

15 = 9k

To solve for k, divide both sides of the equation by 9:

k = 15/9

k = 5/3

Now that we have the value of k, we can substitute it back into the equation y = kx to find the value of y when x is 33:

y = (5/3) * 33

y = 165/3

y = 55

Therefore, when x is 33, y will be 55.