Suppose y varies inversely with x. Write an equation for the inverse variation.
y = 4 when x = 2.5
y = 5 when x = -5
Pls help!? Thx
To write an equation for inverse variation, we can use the formula: y = k/x, where k is the constant of variation.
Given that y varies inversely with x, we can substitute the given values of y and x into the equation to find the value of k.
For the first set of values: y = 4 and x = 2.5
4 = k / 2.5
Multiplying both sides of the equation by 2.5:
10 = k
So, the constant of variation is k = 10.
Now, we can write the equation for inverse variation as:
y = 10 / x
For the second set of values: y = 5 and x = -5
5 = k / -5
Multiplying both sides of the equation by -5:
-25 = k
So, the constant of variation is k = -25.
The equation for inverse variation with this set of values is:
y = -25 / x
Therefore, the equation for the inverse variation in this scenario is:
y = 10 / x for the first set of values, and
y = -25 / x for the second set of values.
Sure! To write an equation for inverse variation, we need to find the constant of variation (k) and then form the equation.
In inverse variation, we know that the product of y and x remains constant, which can be written as y * x = k.
To find k, we can use the given information:
When y = 4 and x = 2.5:
4 * 2.5 = k
10 = k
So, k = 10.
Now, we can write the equation for inverse variation using the value of k:
y * x = 10
However, if you want to solve for y in terms of x, we can rearrange the equation:
y = 10 / x
This is the equation for inverse variation in terms of y and x.
Now, let's check the second set of given values.
When y = 5 and x = -5:
5 * (-5) = k
-25 = k
So, k = -25.
Using this value, the equation for inverse variation becomes:
y = -25 / x
I hope this helps!
inverse variation means that xy = k, a constant.
so, the first is xy=10
and the second is xy = ?