5. Suppose y varies directly with x. Write a direct variation equation that relates x and y.
y=7 1/2 when x=3
A. y=(3/2)x
B. y=(2/3)x
C. y=(5/2)x
D. y=(2/5)x
since y = kx, you have
k = y/x = (7 1/2)/3 = 5/2
so, pick C
To find the direct variation equation that relates x and y, we need to determine the constant of variation.
Since y varies directly with x, we can use the equation y = kx, where k is the constant of variation.
To find k, we can use the given information that y = 7 1/2 when x = 3.
Substituting these values into the equation, we get:
7 1/2 = k * 3
Now, let's solve for k:
To simplify the calculation, let's convert 7 1/2 to an improper fraction:
7 1/2 = 15/2
So the equation becomes:
15/2 = k * 3
To isolate k, divide both sides of the equation by 3:
15/2 / 3 = k
To simplify the fraction division, multiply the numerator and denominator of 15/2 by 1/3:
(15/2) * (1/3) = k
15/6 = k
Now, simplify the fraction:
k = 5/2
So the direct variation equation that relates x and y is:
y = (5/2)x
Therefore, the correct answer is C. y = (5/2)x.