Final answer:
By determining the constant of variation (k=1/32) from the given values, we derived the direct variation equation, y = (1/32)x. Using this equation, we calculated y to be 3/8 when x is 12.
Step-by-step explanation:
Given that y varies directly as x and that y=3/4 when x=24, we can find the constant of variation by using the formula y = kx, where k is the constant of variation. We solve for k by substituting the given values:
y = kx
3/4 = k(24)
Dividing both sides by 24 gives us:
k = (3/4) / 24
k = 1/32
Now that we have the constant of variation, the direct variation equation is y = (1/32)x. To find y when x=12, we substitute 12 for x:
y = (1/32)(12)
y = 12/32
y = 3/8
Therefore, when x=12, y equals 3/8.