If y varies inversely with x, and x = -10 when y = 60. How do you find the inverse variation equation and use it to find the value of y when x = 15?

2 Answers
Feb 17, 2017

Answer:

The equation is #y=-600/x#

At #x=15# the value of #y# is - 40

Explanation:

Set #y=1/x xx k ->k/x#

Given condition #(x,y)->(-10,60)#

So by substitution we have:

#color(green)(y=k/x" "->" " 60=k/(-10))#

Multiply both sides by #color(red)((- 10))#

#color(green)(60color(red)(xx(-10))=k xx(color(red)(-10))/(-10))#

But #(-10)/(-10)=+1#

#-600=k#

Giving: #y=k/x" "->" "y = -600/x#
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Suppose #x=15# as in the question. Then we have:

#y=-600/15 = -40#

Feb 17, 2017

Answer:

#y = -40#

Explanation:

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

#y# varies inversely with #x# can be written as: #" "y prop 1/x#

A proportion can be made into an equation by using a constant:

#y prop 1/x " "rarr" "y = color(red)(k)/x" "rarr" " color(red)(k)= x xx y#

Use the two values given to find the value of #k:#

#color(red)(k) = -10 xx60 =color(red)( -600)#

The equation can therefore be written as: #" "y = color(red)(-600)/x#

Now we know the exact relationship between #x# and #y#

If #x = 15" " y = -600/15 = -40#