-8y = 2x
-7 +9y +7= 2x
Determine whether each equation represents a direct variation. If it does, find the constant of variation.
both do, since there are no constants involved.
To determine whether the equations represent direct variation and find the constant of variation, we need to compare them with the general form of a direct variation equation, which is given by y = kx, where k is the constant of variation.
The first equation, -8y = 2x, can be rewritten as y = -1/4x by dividing both sides by -8. Comparing this to the general form, we see that it represents a direct variation with a constant of variation k = -1/4.
The second equation, -7 + 9y + 7 = 2x, simplifies to 9y = 2x. Dividing both sides by 9, we get y = 2/9x. Comparing this to the general form, we see that it also represents a direct variation with a constant of variation k = 2/9.
To determine whether each equation represents a direct variation, we need to check if the given equations are in the form y = kx, where k represents the constant of variation.
For the first equation -8y = 2x, let's rearrange it in the form y = kx:
Divide both sides of the equation by -8:
y = 2x / -8
y = -1/4x
Since this equation is in the form y = kx, where k = -1/4, it represents a direct variation with a constant of variation -1/4.
Now, let's move on to the second equation -7 + 9y + 7 = 2x. Simplify the equation:
Combine the like terms -7 and +7:
9y = 2x
To put it in the form y = kx, divide both sides by 9:
y = 2x / 9
Since this equation is not in the form y = kx, it does not represent a direct variation. Therefore, it does not have a constant of variation.
To summarize:
The first equation, -8y = 2x, represents a direct variation with a constant of variation -1/4.
The second equation, -7 + 9y + 7 = 2x, does not represent a direct variation.