Question

is the relationship between the variables in the table a direct variation, an inverse variation, or neither? if it is a direct or inverse, write a function to model it. x-9,11,13,15- y- -17, -1,6,27

Answer 1

The relation is neither a direct variation nor an inverse variation.

Explanation:

We will say a relation is direct variation, if increase in one variable causes the other variable to increase and the two variables need to satisfy y=kx else for an increase in variable ,if there is decrease in other variable and the two variables has to satisfy
`y=(k)/(x)`, then it is called inverse variation.

Let us compare the x and y-values in the table.

x is increasing from 9 to 11 to 13 to 15.

And y is also increasing from -17 to -1 to -6 to 27.

Hence the relation is not definitely inverse variation but may be direct variation. Let us check it by finding k for x=9 and x=11.

For x=9, y=-17 that is -17=k(9)

`k=(-17)/(9)`

For x=11, y=-1 that is -1=k(11)

`k=(-1)/(11)`

Since k is different for different pairs it is not direct variation also.