1. determine whether the equation represents a direct variation , if it does find the constant of the vartion
2y=5x+1
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To determine whether the equation represents a direct variation, we need to check if it can be written in the form y = kx, where k is a constant. Let's rearrange the given equation to see if it matches the form:
2y = 5x + 1
Divide both sides of the equation by 2:
y = (5/2)x + 1/2
The given equation can't be written in the form y = kx, as there is an additional constant term of 1/2. Therefore, it does not represent a direct variation.
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To determine whether the given equation represents direct variation, we need to check if it follows the form y = kx, where k is a constant. If the equation satisfies this condition, then it represents direct variation.
Looking at the given equation: 2y = 5x + 1
We need to convert it to the form y = kx. To do this, we will divide both sides of the equation by 2:
2y/2 = (5x + 1)/2
This simplifies to:
y = (5/2)x + 1/2
Comparing this equation to the form y = kx, we see that it does not match. In direct variation, the coefficient of x is the constant of variation (k), but in this equation, the coefficient of x is 5/2, which is not a constant. Therefore, the given equation does not represent direct variation, and we cannot find a constant of variation.