Answer: neither direct variation nor inverse variation.
Explanation:
1) The relation between two variables, y and x, is a direct variation if and only if the quotient between them, y/x, is constant. This is: y / x = k or, equivalently, y = kx.
Note that if y / x is constant, x / y is also constant.
In a direct variation, when x increases, y increases, and when x decreases, y decreases.
2) The relation between two variables, y and x, is an inverse variation if and only if their product, y×x is constant. This is: y × x = k or, equivalently y = k /x or x = k / y.
In an inverse variation when one of the variables increases the other decreases.
3) Writhe the given table and study whether the conditions for direct or inverse variation are met:
x y y/x y×x
-6 -72 -72/(-6) = 12 (-6)(-72) = 432
-4 -47 -47 / (-4) = 11.75 (-4)(-47) = 188
-3 -36 -36 / (-3) = 12 (-3)(-36) = 108
1 12 12 / 1 = 12 (1)(12) = 12
Conclusions;
a) Since neither y / x nor y×x have the same result for every pair, the relation is neither direct nor inverse.
b) Note that if the third pair were (-4, -48) instead of (-4, -47), y / x would be 12, which make a direct variation. In this case the function that modeled it would be:
y = 12x.
