Question

Given that y varies inversely with x, use the values specified to write an

inverse variation equation relating y to x.
x = -20, y = 2

Please help‼️

Answer 1

y = (1/x)+2.05

Explanation:

We are only given one point, so there are an infinite number of possible equations. But forging ahead, we can come up with at least one equation of an inverse relationship containing the point (-20,2).

By inversely, the function will produce lower values of y as x increases, or vice versa. A good first step is to say:

y = 1/x

As the value of x increases, the value of y decreases. Invere accomplished.

Simple, elegant, and inverse. If it were a person, she'd be on the cover of People Magazine.

But we want any equation to include the point (-20,2).

Let's see if we can move y=1/x to include (-20,2)

y=(1/x) + b

2 = (1/(-20)) + b

2 = -(0.05) + b

b = 2.05

The equation y = (1/x)+2.05 is an inverse equation that includes point (-20,2).

See the attached graph. Note that when x = 0, the expression (1/x) becomes (1/0). Division by zero is not allowed (undefined). Use caution if in the neighborhood.