Does 2y = 5x + 1 represent a direct variation?
no. That is always of the form
y = kx
That pesky "+1" messes it up
To determine if an equation represents a direct variation, we need to check if the ratio between the two variables in the equation is constant. In other words, we need to see if the equation can be written in the form y = kx, where k is a constant.
Let's rearrange the given equation 2y = 5x + 1:
2y = 5x + 1
Divide both sides of the equation by 2:
y = (5/2)x + 1/2
Now, we can see that the equation cannot be written in the form y = kx, where k is a constant. The coefficient of x is 5/2, which means it is not a constant.
Therefore, the equation 2y = 5x + 1 does not represent a direct variation.
To determine if the equation 2y = 5x + 1 represents a direct variation, we need to check if the relationship between x and y can be represented by the equation y = kx, where k is a constant.
In the given equation, we don't have a simple y = kx form. We have 2y on the left side instead of y.
To rewrite the equation in the form y = kx, we can divide both sides of the equation by 2:
2y/2 = (5x + 1)/2
Simplifying, we get:
y = (5/2)x + 1/2
Now we have the equation in the form y = kx, where k is 5/2. Therefore, the equation 2y = 5x + 1 represents a direct variation.