How do you write an inverse variation equation given y=-1 when x=-12?

2 Answers
Alan P.
Dec 23, 2016

#color(green)(x * y =12)#

Explanation:

If #x# and #y# form an inverse variation then
#color(white)("XXX")x * y = k# for some constant #k#

Given that #(x=-12,y=-1)# is a solution to the required relation:
#color(white)("XXX")(-12) * (-1) = k#

#rArr k=12#

EZ as pi
Dec 23, 2016

#y = 12/x#

Explanation:

In an inverse variation - or inverse proportion, as one quantity increases the other decreases.

This can be written as: #y prop1/x#

Variations (proportions) are linked by a constant (k)

We can write a variation as an equation by using the constant.

#y = k/x#

#x xx y = k" "larr#now we can find a value for #k# using the values of #x and y# which were given

#k = -12 xx-1 = 12#

The equation is therefore: #y = 12/x#

This is the equation for a hyperbola which is the graph of inverse proportion.

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