Tell whether equation represents direct variation. If so, identify the constant of variation
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To determine if an equation represents direct variation, we need to check if it is in the form y = kx, where y and x are variables and k is a constant. If the equation matches this form, then it represents direct variation, and the constant k is known as the constant of variation.
Let's take an example equation, y = 3x. We can see that this equation is in the form y = kx, where k = 3. Since the equation satisfies the form and has a constant value of 3, it represents direct variation, and the constant of variation is 3.
On the other hand, if we have an equation like y = 2x + 3, it is not in the form y = kx, as it includes a constant term (in this case, 3) which is added to the expression involving x. Therefore, this equation does not represent direct variation.
To identify the constant of variation, it is essential to rearrange the equation in the form y = kx, ensuring that x and y are directly proportional to each other and that there is no term involving x other than the coefficient k.