Question

Please help me with this question

Answer 1

see explanation

Explanation:

the equation for direct variation is

y = kx ← k is the constant of variation

divide both sides by x , then

k =
`(y)/(x)`

calculate k for each ordered pair from the table

k =
`(2)/(-4)` = -
`(1)/(2)`

k =
`(1)/(-2)` = -
`(1)/(2)`

k =
`(-4)/(8)` = -
`(1)/(2)`

since k is constant for all ordered pairs

then the table shows a direct variation with equation

y = -
`(1)/(2)` x

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similarly for the second table

k =
`(5)/(2)`

k =
`(10)/(4)` =
`(5)/(2)`

k =
`(21)/(6)` =
`(7)/(2)`

since k is not constant for all ordered pairs then NOT direct variation