Suppose that y varies inversely with x and that y = 2 when x = 8. What is an equation for the inverse variation?
If y varies inversely with x, it means that y and x have a constant product. Let's call this constant k. Then, we can write:
y * x = k
If we know that y = 2 when x = 8, we can substitute these values into the equation and solve for k:
2 * 8 = k
k = 16
Now we can write the equation for the inverse variation as:
y * x = 16
Or, if we want to solve for y:
y = 16 / x
In order to find the equation for the inverse variation, we can start by identifying the inverse variation equation formula. The inverse variation equation can be written as:
y = k/x
where k is the constant of variation. To find the value of k, we can substitute the given values of y and x into the equation. It is given that when y = 2, x = 8.
2 = k/8
To solve for k, we can multiply both sides of the equation by 8.
2 * 8 = k
16 = k
Now that we have found the value of k, we can substitute it back into the equation to get the equation for the inverse variation.
y = 16/x
Therefore, the equation for the inverse variation is y = 16/x.