Suppose that Y varies directly with X, and Y=4 when X=16
(a) Write a direct variation equation that relates X and Y
(b) Find Y when X=3
To write a direct variation equation that relates X and Y, we can use the formula:
Y = kX
Where k is the constant of variation.
To find the value of k, we can substitute the given values Y = 4 and X = 16 into the equation:
4 = k * 16
To solve for k, divide both sides of the equation by 16:
4/16 = k
Simplifying the fraction, we get:
1/4 = k
So the equation that relates X and Y is:
Y = (1/4)X
Now, to find Y when X = 3, substitute X = 3 into the equation:
Y = (1/4) * 3
Calculating the result:
Y = 3/4
Therefore, when X = 3, Y equals 3/4.
(a) To write the direct variation equation that relates X and Y, we can use the formula for direct variation, which is:
Y = kX
where k is the constant of variation.
Given that Y = 4 when X = 16, we can substitute these values into the equation to solve for k:
4 = k * 16
Dividing both sides by 16, we get:
k = 4/16 = 1/4
Therefore, the direct variation equation for this situation is:
Y = (1/4)X
(b) To find Y when X = 3, we can simply substitute this value into the direct variation equation:
Y = (1/4) * 3
Performing the multiplication, we get:
Y = 3/4
Therefore, when X = 3, Y is equal to 3/4.