Tell whether each equation represents a direct variation. if so, identify the constant of variation.
1. y=4x+9

2. 2y=-8x

3. x+y=0

1. Not a direct variation

2. Direct variation (constant= -4)

3. Direct variation  (constant= -1)

Step-by-step explanation:

A direct variation is a function of the type

y = k*x, where k can be any real number

First case

1. y=4x+9  

The term 9 interferes with the expression (it creates an offset for the value)

2. 2y=-8x  

It is a direct variation, y = -4x

3. x+y=0

It is a direct variation, y = -x

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b