Question

I need help with prob #2 on this

Answer 1

x and y are not in direct variation.

Explanation:

Direct Variation

Two variables x and y have a direct proportion or variation if:

y = k.x

Where k is the factor of proportionality. The value of k must be constant for every ordered pair (x,y). If only one of them does not have the very same k, then the relationship is not direct.

The value of k can be solved from the equation:

`\displastyle k=(y)/(x)`

Let's substitute the given points in the table:

(2,8)

`\displastyle k=(8)/(2)=4`

k = 4

(4,16)

`\displastyle k=(16)/(4)=4`

k = 4

(6,30)

`\displastyle k=(30)/(6)=5`

k = 5

Since the value of k is not constant, then x and y are not in direct variation.