Question

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

Answer 1

A direct variation is of the form
y = kx
where k is the constant of variation

In most cases k is positive in which case
y increase in direct proportion to an increase in x
Example
k = 2
x = 1,       y = kx = 2(1)= 2
x = 3,       y = kx = 2(3) = 6


Occasionally k is negative in which case
y decreases in direct proportion to an increase in x
Example
k = -2
x = 1,       y = kx = (-2)(1) = -2
x = 3,       y = kx = (-2)(3) = -6
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This is not to be confused with an indirect variation which is of the form
y = k/x
where k is the constant of variation
Example

When k is positive y decreases inversely as x increases
k = 2
x = 1,       y = k/x = 2/1 = 2
x = 3, y = k/x = 2/3 = 2/3

When k is negative y increases inversely as x increases
k = -2
x = 1,       y = k/x = -2/1 = -2
x = 3        y = k/x = -2/3 = -2/3