I am doing Direct Variation in math. I don't understand how to do it. It would be very helpful if you helped me with these problems:

Is each equation a direct Variation? If it is, find the constant of variation:

y=3/5x

-3x+2y=0

-5x+2y=9

8x+4y=12

the first one is K=3/5

To determine if an equation represents direct variation, you need to check if it follows the form "y = kx," where "k" represents the constant of variation. If an equation matches this form, it is a direct variation. If it does not, it is not a direct variation.

Let's analyze each equation one by one:

1. y = (3/5)x
This equation matches the form y = kx, where k = 3/5. Therefore, it is a direct variation.

2. -3x + 2y = 0
To check if this equation represents direct variation, rearrange it in the form y = kx: 2y = 3x. Divide both sides by 2 to isolate y: y = (3/2)x. Since this equation follows the form y = kx, it is a direct variation with k = 3/2.

3. -5x + 2y = 9
Similarly, rearrange the equation to isolate y: 2y = 5x + 9. Divide both sides by 2: y = (5/2)x + (9/2). This equation does not match the form y = kx because there is an additional constant term. Hence, it is not a direct variation.

4. 8x + 4y = 12
Reorganize the equation to isolate y: 4y = -8x + 12. Divide both sides by 4: y = (-8/4)x + (12/4). Simplify: y = -2x + 3. This equation does not follow the form y = kx since there is a coefficient for x rather than just a constant. It is not a direct variation.

To summarize:

1. Direct Variation with k = 3/5: y = (3/5)x
2. Direct Variation with k = 3/2: -3x + 2y = 0
3. Not a direct variation: -5x + 2y = 9
4. Not a direct variation: 8x + 4y = 12