Find the variation constaant and an equation of variation where Y varies directly as X and Y = 72 hen X = 8

The variation constant is K = ?
The equation of variation is Y = ?

I think that K = 9 but not sure
I don't have a clue about the rest.

Thank you, I thought I was on the right track but wasn't sure.

solution:

y=kx
72=k(8)
72/8=k
9=k

so 9 is our constant...

To find the variation constant (K) and the equation of variation, we need to understand the concept of direct variation. When two variables, Y and X, vary directly, it means that as one variable increases or decreases, the other variable also increases or decreases by the same factor.

The equation of direct variation is given by the formula:
Y = K * X

In this case, we are given that when X = 8, Y = 72. To find the variation constant (K), we can substitute the given values into the equation:

72 = K * 8

To solve for K, divide both sides of the equation by 8:

K = 72 / 8
K = 9

Therefore, the variation constant (K) is indeed 9.

To determine the equation of variation, substitute the value of K into the equation:
Y = 9X

Thus, the equation of variation for this problem is Y = 9X.

"Y varies directly as X" ----> y = kx

but we are given x=8, y = 72
72 = k(8)
k = 9, so

y = 9x

all done!