Here is the question :
Determine whether the equation represents direct, inverse, joint, or combined variation. y=2x^3
y varies directly as x^3
To determine whether the equation represents direct, inverse, joint, or combined variation, we need to compare the equation to the general forms of each type.
1. Direct Variation: A direct variation equation takes the form y = kx, where k is a constant. The variables y and x are directly proportional, meaning as one increases, the other also increases proportionally.
2. Inverse Variation: An inverse variation equation takes the form y = k/x, where k is a constant. The variables y and x are inversely proportional, meaning as one increases, the other decreases proportionally.
3. Joint Variation: A joint variation equation takes the form y = kxm, where k is a constant and m is an exponent. The variables y and x are related in a way where one or both can vary simultaneously.
4. Combined Variation: A combined variation equation combines direct and inverse variation. It takes the form y = kx/z, where k is a constant and z is another variable.
Given the equation y = 2x^3, we can see that the equation includes only one variable (x) raised to a power (3), indicating that it follows the form of joint variation. Therefore, the equation represents joint variation.