Yvaries inversely as x, and y = 50 when x = 10. what is the value of y when x = 20?

If Y varies inversely as x, then as y increases, x decreases or vice versa. It can be represented by an equation as:

y α 1/x

We add a proportionality constant k in order  to change it to an equality.

y = k/x

We then solve for k by substituting the first condition to the equation.

y = k/x
50 = k/10
k = 500

When x = 20, then:

y = 500/x
y = 500/20
y = 25

Geometric pattern of 2 i’m guessing. not really sure about what you’re asking but i hope this !