Determine whether the equation represents direct, inverse, joint, or combined variation. y = 2x on 3rd
To determine the type of variation represented by the equation y = 2x on 3rd, we need to understand the different types of variations.
1. Direct Variation: In direct variation, one variable (y) is directly proportional to another variable (x). The equation can be written in the form y = kx, where k is a constant.
2. Inverse Variation: In inverse variation, one variable (y) is inversely proportional to another variable (x). The equation can be written in the form y = k/x, where k is a constant.
3. Joint Variation: In joint variation, one variable (y) varies jointly with two or more other variables (x1, x2, x3, etc.). The equation can be written in the form y = kx1x2x3..., where k is a constant.
4. Combined Variation: Combined variation combines both direct and inverse variation. The equation can be written in the form y = kx/x1, where k is a constant.
Now, let's analyze the given equation: y = 2x on 3rd.
The "on 3rd" part suggests that there is another variable involved. Let's assume this variable is z. Rewriting the equation, we get y = 2xz.
Comparing it with the forms of variation:
- It is not a direct variation since there is an extra variable (z) involved.
- It is not an inverse variation since the equation is not in the form of y = k/x.
- It is not a joint variation since there is only one extra variable (z), not two or more.
Therefore, the equation y = 2x on 3rd represents combined variation because it combines both direct (2x) and inverse (1/z) variations.