Question

Determine if the values in the table are proportional by finding the constant of proportionality (k). Show your work to indicate what the constant (k) is.

Write an equation to show that y is directly proportional to x using the constant.

Determine the value of y if x = 6.

Answer 1

The values in the table are proportional with the constant of proportionality
`k=2.5`

For the given table the equation can be written as :

`y=2.5x`

The value of
`y=15` when
`x=6`

Explanation:

From a given data with points
`(x,y)` the constant of proportionality
`k` can be calculated as:

`k=(y)/(x)`

For the given data we will find the constant of proportionality
`k` for each point.

1)
`(1,2.5)`

`k=(2.5)/(1)=2.5`

2)
`(2,5)`

`k=(5)/(2.5)=2.5`

3)
`(3,7.5)`

`k=(7.5)/(3)=2.5`

4)
`(4,10)`

`k=(10)/(4)=2.5`

We see that for each set of points we get the same value of
`k`. This shows that the values in the table are proportional with the constant of proportionality
`k=2.5`

The equation of
`y` directly proportional to
`x` can be written as :

`y=kx`

where
`k` is the constant of proportionality

For the given table the equation can be written as :

`y=2.5x`

To find value of
`y` when
`x=6`, we will plugin 6 in place of
`x` in the equation and solve for
`y`

So, we have.

`y=2.5*6=15`

So, value of
`y=15` when
`x=6`