Question

If the point (4,-2) is included in a direct variation relationship, which point also belongs in this direct variation? A. (-4,2) B. (-4,-2) C. (2,-4) D. (-2,4)

Answer 1

(-4,2) belongs in this direct variation.

Explanation:

Let the direct variation relationship is expressed by the equation y = mx ........ (1), where x and y are in direct variation and k is the variation constant.

Now, the point (4,-2) is included in the direct variation relationship, then from equation (1) we get, -2 = 4m

⇒
`m =  - (1)/(2)`

Therefore, the equation (1) becomes
`y = - (1)/(2)x`

⇒ x + 2y = 0 ......... (2)

Now, from the given four options only the point (-4,2) satisfies the relation (2).

Hence, (-4,2) belongs in this direct variation. (Answer)