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

ad = ae + ed = y + 7

similar triangles therefor

ac/ab = ad/ae

6/4 = (y + 7) / y

cross multiply

6y = 4(y + 7)

6y = 4y + 28

2y = 28

y = 14

step-by-step explanation:

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.