Find the variation constant and an equation of variation where y varies inversely as x and y equal 9 when x equals 16

The statement "y varies inversely as x means that when x increases, y decreases by the same factor. In other words, the expression xy is constant :

x*y = k

k is the variation constant.

Just substitute the values in that formula :

16*9 = 4*4*9 = 172.

So the variation constant here is 172.

In order to find the equation of variation of y, you should change the equation i gave you.

y = k/x
y= 172/x

Hope this helps !

Photon

Let's do both. For the first one, we can add 1 to both sides using the property of equality, and get 4x < -12. Then, we divide by 4, getting us x<-3. For the second, we subtract 3 from both sides to get -2x < 4. Then, we divide by -2 on both sides, but when we divide by a negative we have to switch the sign. So, we get x > -2. Hope this helps.