Which of the following represents a direct variation function?
The answer coices are
A)d=2r
B)y=9x+1
C)y=-3
D)a=1/2h(b1+b2)
A direct variation should
1. be a linear function of one variable
2. passes through the origin (0,0), i.e. if the independent variable is set to zero, the dependent variable should also be zero.
If you examine the four choices according to the above criteria, you will be able to eliminate all but the required function.
-4 + 7x + 4 = 3y
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To determine which equation represents a direct variation function, we need to understand what a direct variation function is.
A direct variation function is a type of equation that represents a linear relationship between two variables. It can be expressed in the form y = kx, where y and x are the variables, and k is a constant called the constant of variation.
Let's analyze each option to determine if it represents a direct variation function:
A) d = 2r
This equation does not represent a direct variation function because it does not follow the form y = kx. Instead, it represents a linear relationship between d and r with a constant ratio of 2.
B) y = 9x + 1
This equation does not represent a direct variation function because it includes an additional constant term (1) alongside the coefficient of x (9). In direct variation, there is no constant term.
C) y = -3
This equation does represent a direct variation function because it follows the form y = kx. In this case, the constant of variation (k) is -3, indicating a linear relationship with a constant ratio of -3.
D) a = (1/2)h(b1 + b2)
This equation does not represent a direct variation function because it includes additional variables (h, b1, b2) alongside the coefficient (1/2). Direct variation functions only involve two variables.
Therefore, the correct answer is C) y = -3, as it represents a direct variation function with a constant of variation equal to -3.