Hi, my name is Ashley...I'm from Lakeland, Florida, and attend McKeel Academy 9th grade in Algebra...and I'm stuck on this unit of direct and inverse variation..please and my problems and show me how to do each PLEASE!!!

Assume that y varies directly as x

If y= -4 when x = 2, find y when x= -6
If y= -5 when x= 12.5, find x when y=15
If y= 16 when x= 4, find y when x=6
If y = 198 when x=22, find y when x=182

Assume that y varies inversely as x

If y =-4 when x=2, find y when x =-6
If y=6 when x=-4, find x when y=12/5
If y=27 when x=12, find x when y= -12
If y= 60 when x=80, find x when y=-20

Hi Ashley,

We say y varies directly as x, or equivalently, y is proportional to x, when there exists a constant k such that y = kx (k is the constant of variation.)

For your first problem y= -4 when x = 2 and hence -4 = k (2). Thus k = -2. This same constant, k = -2, is valid for the pair x,y when x = -6. That is y =k (-6) = (-2)(-6) = 12.

For the "inverse" situation where y goes down as x goes up we say y is inversely proportional to x, or equivalently, y varies inversely as x, to mean that there exists a constant k for which xy = k. Equivalently,

y = k/x = k(1/x),

Thus for you problem "if y =-4 when x=2, find y when x =-6", xy = k so (2)(-4) = k and hence k = -8. Thus, when x = -6, (-6)y = -8 so y = 4/3

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