Question

Find the constant of variation k for the direct variation. x f(x) –1 2 0 0 2 –4 5 –10

Answer 1

`k=-2`

Explanation:

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

a) For
`x=-1`

`f(x)=2`

Find the value of k

`f(x)/x=k` ------> substitute the values

`k=2/-1=-2`

b) For
`x=2`

`f(x)=-4`

Find the value of k

`f(x)/x=k` ------> substitute the values

`k=-4/2=-2`

c) For
`x=5`

`f(x)=-10`

Find the value of k

`f(x)/x=k` ------> substitute the values

`k=-10/5=-2`

therefore

`k=-2`

Answer 2

For direct variation,
f(x) = k*x
You have
2 = k*(-1)
The value of k can found by multiplying by -1.
k = -2