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

Answer 1

The inverse variation equation can be written as y = k/x, where k is a constant. To find the value of k, substitute the given values of x and y into the equation and solve for k. In this case, when x = -12 and y = -1, the equation becomes -1 = k/(-12). Solving for k, we get k = 12. Therefore, the inverse variation equation is y = 12/x.

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Answer 2

Hazel Anglin

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

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#

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Answer 3

Abigail Allen

#y = 12/x#

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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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.