Question

"The value of y varies directly with x. When y= 3 3/4 , x= 3/4 .

What is the value of y when x is 1/2?
A) 1 1/4
B) 2 1/2
C) 4 1/4
D) 4 3/4

Answer 1

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.