Determine whether the equation represents a direct variation.
2y=5x+1
Not a direct variation
Direct variation, constant of variation is 5/2
Direct variation, constant of variation is 2/5
Direct variation, constant of variation is 1- 2/5
What’s the answer to the whole test
To determine whether the equation represents a direct variation, we need to compare the equation's form to the general form of a direct variation equation, which is y = kx, where k is the constant of variation.
The equation given is 2y = 5x + 1. To make it look like the general form, we can divide both sides of the equation by 2: y = (5x + 1)/2.
Comparing this to the general form, we see that the equation does not match because there is a fraction (5/2) on the right side instead of a constant (k) next to x.
Therefore, the equation 2y = 5x + 1 does not represent a direct variation.
To determine whether an equation represents a direct variation, we need to check if it can be written in the form y = kx, where k is a constant called the constant of variation.
In the given equation, 2y = 5x + 1, we can isolate y by dividing both sides of the equation by 2:
(2y)/2 = (5x + 1)/2
Simplifying, we get:
y = (5/2)x + 1/2
Comparing this equation with the form y = kx, we can see that the value of k is (5/2).
Therefore, the equation 2y = 5x + 1 represents a direct variation with a constant of variation of 5/2.
it does not
a direct variation has the form y = kx