Question

Suppose that x and y vary inversely, and x = 10 when y = 8. Write the function that models the inverse variation.
a. y=2/x
b. y=18/x
c. y=80/x
d. y=0.8x

Answer 1

Answer:

c. $y=\frac{80}{x}$

Step-by-step explanation:

Given:

$x$ and $y$ vary inversely.

Therefore, we can express y in terms of x as:

$y=\frac{k}{x}$

Where, $k$ is a constant of proportionality.

Now, at $x=10,y=8$

Plug in 10 for $x$ and 8 for $y$ in the above equation and solve for $k$.

This gives,

$8=\frac{k}{10}\\k=8\times 10=80$

Therefore, the function that models the inverse variation is :

$y=\frac{k}{x}\\y=\frac{80}{x}$.