For each equation, determine whether it shows a direct variation (that is, shows directly proportional variables).
If it does, find the constant of variation and write it in simplest form.
2x-7y=8 k=
8x-5y=0 k=
To determine if an equation shows direct variation, we can rewrite it in the form y = kx, where k is the constant of variation.
For the equation 2x - 7y = 8:
First, isolate y by subtracting 2x from both sides:
-7y = -2x + 8
Next, divide everything by -7 to solve for y:
y = (2/7)x - 8/7
Since the equation can be expressed as y = (2/7)x, it shows direct variation. The constant of variation is k = 2/7.
For the equation 8x - 5y = 0:
First, isolate y by subtracting 8x from both sides:
-5y = -8x
Next, divide everything by -5 to solve for y:
y = (8/5)x
Since the equation can be expressed as y = (8/5)x, it shows direct variation. The constant of variation is k = 8/5.