To determine if y varies directly with x, we need to rewrite the equation in a form that allows us to explore the relationship between the two variables. The given equation is:
5y = 5x + 10
First, let’s isolate y by dividing all terms by 5:
y = x + 2
Now, we can see that this equation represents a linear relationship between y and x. However, for y to vary directly with x, it must be in the form:
y = kx
Where k is the constant of variation. In our case, the term +2 indicates that y does not vary directly with x because there is a constant added to the equation. Therefore, y does not vary directly with x.
In a direct variation scenario, as x changes, y would also change proportionally without any constant term added or subtracted. Since there is a +2 in our equation, y depends on x, but not in a directly proportional way.
In conclusion, the answer is: no, y does not vary directly with x in this case, and the constant of variation k cannot be determined as there is no direct variation present.