Question

Is y is proportional to x?What’s the constant of proportionality (k)?K = y/xWhat’s the equation that represents the table?

Answer 1

For two numbers to be proportional, they must verify:

`y=kx`

"y is proportional to x"

In this case, to verify this, we nedd to calculate if each value of y can be founded by multiplying x by a constant k.

If y = kx is true, then:

`k=(y)/(x)`

And if k is the same for al pairs (x, y) then the relationship is proportional.

Using the table we do:

`\begin{gathered} k=(2)/(12)=(1)/(6) \\ k=(3)/(18)=(1)/(6) \\ k=(4)/(24)=(1)/(6) \\ k=(5)/(30)=(1)/(6) \end{gathered}`

Since k is the same for all pair of values, y is proportional to x.

Also we have already calculated k = 1/6

And the equation that represents the table is:

`y=(1)/(6)\cdot x`