Final answer:
The value of y is found by first determining the constant of variation (k) when y is 3 3/4 and x is 3/4. Using k, we then find y when x is 1/2, resulting in y equaling 2 1/2 (option B).
Step-by-step explanation:
The student's question is about direct variation between two variables. In this case, the relationship between y and x is given by the equation y = kx, where k is the constant of variation. We know that when y=3¾ (which is 3.75 in decimal form), x=¾ (which is 0.75 in decimal form).
First, we need to find the constant of variation k by dividing the given value of y by the given value of x.
To find k: k = y/x = 3.75/0.75 = 5. Once we have k, we can use it to find the value of y when x is 1/2.
Now, solving for y when x is 1/2:
y = kx = 5 × 0.5 = 2.5, which can be written as 2½ in fraction form.
Therefore, the value of y when x is 1/2 is 2 1/2, which corresponds to option B.