Question

I need this asap ty:p

Which of the following equations are equations of a direct variation? Choose all that apply.
(a) x=−2y
(b) x+2y=12
(c) 3x−2y=0
(d) 5x^2+y=0
(e) y =0.3x +1.6
(f) y−2=x

Answer 1

(a) x = -2y

(c) 3x - 2y = 0

Step-by-step explanation:

You can tell if an equation is a direct variation equation if it can be written in the format y = kx.

Note that there is no addition and subtraction in this equation.

Let's put these equations in the form y = kx.

(a) x = -2y

y = x/-2 → y = -1/2x

This is equivalent to multiplying x by -1/2, so this is an example of direct variation.

(b) x + 2y = 12

2y = 12 - x

y = 6 - 1/2x

This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is NOT an example of direct variation.

(c) 3x - 2y = 0

-2y = -3x

y = 3/2x

This follows the format of y = kx, so it is an example of direct variation.

(d) 5x² + y = 0

y = -5x²

This is not in the form of y = kx, so it is NOT an example of direct variation.

(e) y = 0.3x + 1.6

1.6 is being added to 0.3x, so it is NOT an example of direct variation.

(f) y - 2 = x

y = x + 2

2 is being added to x, so it is NOT an example of direct variation.

The following equations are examples of direct variation:

x = -2y

3x - 2y = 0

Answer 2

(a) x = -2y

(c) 3x - 2y = 0

Explanation:

You can tell if an equation is a direct variation equation if it can be written in the format y = kx.

Note that there is no addition and subtraction in this equation.

Let's put these equations in the form y = kx.

(a) x = -2y

• y = x/-2 → y = -1/2x
• This is equivalent to multiplying x by -1/2, so this is an example of direct variation.

(b) x + 2y = 12

• 2y = 12 - x
• y = 6 - 1/2x
• This is not in the form y = kx since we are adding 6 to -1/2x. Therefore, this is NOT an example of direct variation.

(c) 3x - 2y = 0

• -2y = -3x
• y = 3/2x
• This follows the format of y = kx, so it is an example of direct variation.

(d) 5x² + y = 0

• y = -5x²
• This is not in the form of y = kx, so it is NOT an example of direct variation.

(e) y = 0.3x + 1.6

• 1.6 is being added to 0.3x, so it is NOT an example of direct variation.

(f) y - 2 = x

• y = x + 2
• 2 is being added to x, so it is NOT an example of direct variation.

The following equations are examples of direct variation:

• x = -2y
• 3x - 2y = 0