Question

Which of the following ordered pairs represent a direct variation. Find the missing value. 1. (32, 80) and (x, 100) x = _____ 2. (-28,-7) and (20, y) y = _____

Answer 1

When having an ordered pair, we say they are in direct variation if the quotient:

`(y)/(x)`

is constant. For case 1 we have:

`(80)/(32)=(100)/(x)`

we can solve for "x" by multiplying by "x" on both sides:

`(x80)/(32)=100`

Now we multiply by 32/80 on both sides:

`x=(100*32)/(80)`

Solving the operations we get:

`x=40`

For case 2 we have:

`-(7)/(-28)=(y)/(20)`

Now we solve for "y" by multiplying by 20 on both sides:

`(-7*20)/(-28)=y`

Solving the operations:

`y=5`