-3x+2y=0
-5x+2y=9
8x+4y=12
Is each equation a direct Variation? If it is, find the constant.
-3x+2y=0 is a direct variation, meaning that y is proportional to x.
The proportionality factor is m.
y = mx
In this case y = (3/2) x, so m = 3/2
8x+4y=12
To determine if an equation represents direct variation, we need to check if the ratio of the variables remains constant.
Let's analyze each equation separately:
1) -3x + 2y = 0
To determine if this equation represents direct variation, we need to isolate y. We can start by moving -3x to the other side of the equation:
2y = 3x
Next, we divide both sides of the equation by 2 to solve for y:
y = (3/2)x
Since y is directly proportional to x with a constant ratio of 3/2, we can conclude that this equation represents direct variation, and the constant of variation is 3/2.
2) -5x + 2y = 9
Similarly, we isolate y by moving -5x to the other side of the equation:
2y = 5x + 9
Dividing both sides by 2, we get:
y = (5/2)x + 9/2
Since y is not directly proportional to x (the coefficient of x is not constant), this equation does not represent direct variation. There is no constant of variation in this case.
3) 8x + 4y = 12
Again, we isolate y by moving 8x to the other side of the equation:
4y = -8x + 12
Dividing both sides by 4, we get:
y = -2x + 3
Similar to the second equation, y is not directly proportional to x, so it does not represent direct variation.
In summary:
- The first equation, -3x + 2y = 0, represents direct variation with a constant of variation of 3/2.
- The second equation, -5x + 2y = 9, does not represent direct variation.
- The third equation, 8x + 4y = 12, also does not represent direct variation.