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:

$k=\frac{y}{x}$

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

Using the table we do:

$\begin{gathered} k=\frac{2}{12}=\frac{1}{6} \\ k=\frac{3}{18}=\frac{1}{6} \\ k=\frac{4}{24}=\frac{1}{6} \\ k=\frac{5}{30}=\frac{1}{6} \end{gathered}$

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:

$y=\frac{1}{6}\cdot x$