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
I will do one, and you do the rest. I will be happy to critique them.
-5x+2y=9
add 5x to both sides.
2y=5x+9
divide both sides by 2
y=2.5 x + 4.5
Yes, direct variation, constant of variation is 2.5
6x+2y=0
To determine whether an equation represents direct variation, you need to check if it follows the form y = kx, where k is the constant of variation.
Let's analyze each equation one by one:
1. y = (3/5)x
This equation is a direct variation because it follows the form y = kx. The constant of variation (k) is 3/5.
2. -3x + 2y = 0
This equation is not in the form y = kx. To determine if it represents direct variation, we need to rewrite it in slope-intercept form (y = mx + b) or solve it for y. Let's rearrange the equation:
2y = 3x
y = (3/2)x
The equation y = (3/2)x represents direct variation, and the constant of variation (k) is 3/2.
3. -5x + 2y = 9
This equation is not in the form y = kx. Let's solve it for y:
2y = 5x + 9
y = (5/2)x + 9/2
The equation y = (5/2)x + 9/2 does not represent direct variation because it doesn't have the form y = kx.
4. 8x + 4y = 12
This equation is not in the form y = kx. Solving it for y:
4y = -8x + 12
y = -2x + 3
The equation y = -2x + 3 does not represent direct variation because it doesn't have the form y = kx.
Therefore, only the first equation, y = (3/5)x, represents direct variation. The constant of variation (k) for that equation is 3/5.