Question

Direct variations need help

Answer 1

Part 11) The table represent a direct variation. The equation is
`y=18x`

Part 12) The table represent a direct variation. The equation is
`y=0.4x`

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Part 11)

For x=0.5, y=9

Find the value of k

`k=y/x` ----->
`k=9/0.5=18`

For x=3, y=54

Find the value of k

`k=y/x` ----->
`k=54/3=18`

For x=-2, y=-36

Find the value of k

`k=y/x` ----->
`k=-36/-2=18`

For x=1, y=18

Find the value of k

`k=y/x` ----->
`k=18/1=18`

For x=-8, y=-144

Find the value of k

`k=y/x` ----->
`k=-144/-8=18`

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

`y=18x`

Part 12)

For x=-5, y=-2

Find the value of k

`k=y/x` ----->
`k=-2/-5=2/5=0.40`

For x=3, y=1.2

Find the value of k

`k=y/x` ----->
`k=1.2/3=0.40`

For x=-2, y=-0.8

Find the value of k

`k=y/x` ----->
`k=-0.8/-2=0.4`

For x=10, y=4

Find the value of k

`k=y/x` ----->
`k=4/10=0.4`

For x=20, y=8

Find the value of k

`k=y/x` ----->
`k=8/20=0.4`

The values of k is the same for each ordered pair

therefore

The table represent a direct variation

The linear equation is

`y=0.4x`