Answer:
(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
