Writing: For a direct variation, describe how the constant of variation affects whether y increases or decreases as x increases.

Answer 1

Direct variation means that there is a common ratio. If the ratio is positive, x increasing makes y increase. An example is y = 2x. If the ratio is negative, x increasing makes y decrease. An example is y = -2x. The ratio is the slope of the line, which in calculus is a derivative. If you add a constant term to make something like y = 2x + 3, each chance in x makes double the change in y, but the ratio of y/x varies, whereas in y = 2x the ratio of y/x is always 2. I know the concept, but without seeing a definition of "direct variation" and "constant of variation" I don't know if the equations can have constant terms. All equations with direct variation are lines. x and y will always be to the first power, with no exponent shown because a number to the first power is itself. There will never be terms like 1/x or x^2. They will never be curves or change direction, and they will be defined for every value of x and y without any asymptotes.