if y varies inversely as x find the constant of variation k and the inverse variation equation for the solution y=1/7 when x=35

Question

I would really appreciate it if someone helped me out with this problem!! Thank you!!

Answer 1

Dear Jocelyn,

    The trick is to remember the equation, XY=K.  Inversely simply means that has one variable increases, the other decreases.

 

Let me give you a different example:   If y varies inversely as X find the constant of variation K and the inverse variation equation for the solution y=1/2 when X=44.

 

 

XY= K     Just substitute the values into the equation:  44(1/2)=K         44/2=22=K, so  rewrite the XY=K to the following:   Y=K/x       Y=22/X , and you are done.

 

 

 

Now, let's try your problem:    XY=K      Given:  y=1/7   when X=35

 

You are asked to find two things, the constant of variation K and the inverse variation equation.

 

Use substitution:            35* 1/7 =K                 35/7=5=K

 

                                   XY=K     is rewritten as    Y=K/X   Use this equation for the substitution.  

 

Just substitute for K and X.  Leave Y as Y and you are done.

 

If I helped you, please give me a thumbs up.

 

                                                                       Susan C.