if y varies inversely as x, find the constant variation k and the inverse variation equation for the situation.

Question

y=1/5 when x=35

Answer 1

The inverse variation equation is y = k / x.

We're told that that the point (35, 1/5) satisfies this equation, so

1/5 = k / 35 => k = 7, and y = 7/x.

Answer 2

y=k/x

substitute the x, y values into the inverse equation

1/5=k/35

cross multiply

5k=35 divide by 5

k=7

substitute 7 for k in the original inverse equation

y=7/x as a function of x y=f(x)=7/x

or x=7/y for the original equation as a function of y x=f(y)=7/y

you could graph this as a standard hyperbola rotated 45 degrees xy=7, with 2 branches of the hyperbola in the 1st and 3rd quadrant, vertices at (7^1/2, 7^1/2) and (-7^1/2, -7^1/2) centered at the origin, symmetric over the origin, with x and y axes as the asymptotes.

if I understand your question correctly. Not certain I do.

Answer 3

y = k/x

1/5 = k/35

(1/5)(35) = k

k = 7

y = 7/x