Question

If ( y ) varies directly with ( x ) and ( x = 13 ) when ( y = 117 ), what is the ( k ) value?

a) ( k = 9 )
b) ( k = 10 )
c) ( k = 11 )
d) ( k = 12 )

Answer 1

To find the constant of variation k in a direct relationship where x = 13 and y = 117, we substitute these values into the equation y = kx, resulting in k = 117 / 13, which simplifies to k = 9.

Step-by-step explanation:

When y varies directly with x, the relationship between the two variables can be represented by the equation y = kx, where k is the constant of variation. To find the value of k, we use the given values of x = 13 and y = 117 and substitute them into the direct variation equation.

y = kx

117 = k(13)

To solve for k, divide both sides of the equation by 13:

k = 117 / 13

k = 9

Therefore, the value of the constant k is 9, which corresponds to option a.