Question

Which of the following equations is an example of direct variation?

y + 10 = 2(x + 5)
y = 2(x + 5)
y + 5 = 2(x + 5)
y = x + 5

Please help!

Answer 1

Direct variation is when x/y = constans
That's mean, that formula of direct variation is y=kx (k inequal 0)

First:
y+10=2(x+5)
y+10 = 2*x + 2*5
y+10=2x+10 /subtract 10
y=2x
It is y=kx. Here k=2 - it is example of direct variation.

Next:
y=2(x+5)
y=2*x + 2*5
y=2x+10
It is not y=kx (because you've got +10). So it isn't.

Next:
y+5=2(x+5)
y+5=2x+10 /subtract 5
y=2x+5
It isn;t too, because you've got +5.

Next:
y=x+5 isn't, because you've got +5.

So only first equation

Answer 2

y + 10 = 2(x + 5)

Explanation:

Direct variation is a mathematical relationship between any two variables which can be expressed by equation in which one of the variable is equal to a constant times of the other variable.

So, y = kx

where k is any number.

Considering A as:

y + 10 = 2(x + 5)

Solving,

y = 2x , this is a direct variation.

Considering B as:

y = 2(x + 5)

Solving,

y = 2x + 10, this is not a direct variation.

Considering C as:

y + 5 = 2(x + 5)

Solving,

y = 2x + 5, this is not a direct variation.

Considering D as:

y = x + 5, this is not a direct variation.