Question

Is someone able to do this really quick thanks :)

Answer 1

`y = (3)/(4) x`, x and y show direct variation.

Explanation:

Step 1:

For x and y to show direct variation, they should be proportional to each other.

This means for x and y to be in direct variation, they should be of the form
`y=kx,` where k is the constant of proportionality.

If we simplify the given equation and get an equation similar to
`y=kx`, x and y show direct variation.

Step 2:

Now we simplify the given equation,

`y + (3)/(2) = (3)/(4) (x+2),`

`y + (3)/(2) = (3)/(4) x + (3)/(4) (2) = (3)/(4) x+ (3)/(2) .`

`y + (3)/(2) = (3)/(4) x+(3)/(2) .`

If we subtract
`(3)/(2)` from both sides, we get

`y = (3)/(4)x.`

This is of the form
`y=kx` where
`k = (3)/(4) .` So x and y show direct variation.