if y varies inversely with x' find the constant of variation and write an equation if y=1/2 and x=-10
since xy = k is constant,
k = (1/2)(-10)
To find the constant of variation, we use the formula for an inverse variation:
y = k/x
where k is the constant of variation.
Now, let's substitute the given values into the equation:
1/2 = k/(-10)
To isolate k, we can cross multiply:
1/2 * -10 = k
-10/2 = k
-5 = k
Therefore, the constant of variation is -5.
To write the equation of variation, we substitute the constant of variation back into the equation:
y = -5/x
To find the constant of variation when y varies inversely with x, we can use the formula:
k = y * x
where k is the constant of variation, and y and x are the given values.
In this case, we have y = 1/2 and x = -10. Let's substitute these values into the formula to find the constant of variation:
k = (1/2) * (-10)
k = -5
So, the constant of variation is -5.
Now, to write the equation that describes the inverse variation between y and x, we can use the following formula:
y = k / x
Substituting the value of k, we have:
y = -5 / x
Therefore, the equation that represents the inverse variation between y and x is y = -5 / x.