Question

Given the following set of ordered pairs, determine if it is direct or inverse variation and find the value of k. (2, -10) (4, -20) (7, -35) (8, -40)

Answer 1

direct variation

Explanation:

The constant of variation k for direct variation is

k =
`(y)/(x)`

Calculate this ratio for each set of points

`(-10)/(2)` =
`(-20)/(4)` =
`(-35)/(7)` =
`(-40)/(8)` = - 5

Then ordered pairs are in direct variation with k = - 5

The constant of variation for inverse variation is

k = xy

2 × - 10 = - 20

4 × - 20 = - 80

7 × - 35 = - 245

8 × - 40 = - 320

There is no constant thus not inverse variation