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How do you write the equation of a direct variation that includes the point (-6,1)?

Answer 1

Genesis Allen

Equation of direct variation is:#" "y=(-1/6)x#

Let #(x,y) ->(-6,1)#

The term 'direct variation implies that we have the structure of

Let #k# be a constant of variation

Then #y=kx#....................(1)

We are given that #(x,y)->(-6,1)# so by substitution equation (1) becomes

#1=k(-6)#

Divide both sides by -6

#1/(-6)=kxx(-6)/(-6)#

But #(-6)/(-6)=1# giving

#-1/6=k# '~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Equation of direct variation is:#" "y = kx" "->" "y=(-1/6)x#

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Answer 2

Jace Anderson

The equation of a direct variation can be written in the form y = kx, where k is the constant of variation. To find k, plug in the given point (-6,1) into the equation and solve for k:

1 = k(-6)

k = -1/6

Therefore, the equation of the direct variation that includes the point (-6,1) is y = (-1/6)x.

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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.