Question

Y varies directly as x, and y = 22.5 when x = 0.9. Write a direct variegation equation for this situation

Answer 1

`y=25x`

Explanation:

Function Models

There are times where we are interested in expressing data sets into mathematic models. One of the most commonly used is the linear model, where the dependent variable has a linear relation with the independent variable. A special case of a linear model is the direct relation or proportion, where the variables relate in the form:

`y=kx`

Where k is an arbitrary constant.

We know y=22.5 when x=0.9. This can be used in the equation above to find the value of k:

`22.5=k(0.9)`

Solving for k:

`\displaystyle k=(22.5)/(0.9)=25`

The equation that models the relation is:

`\boxed{y=25x}`