Question

If y varies directly as the cube of x, what is the value of y in these ordered pairs?

(4,16) and (2, y)

Answer 1

Well if y varies directly as the cube of x we have

\[y = kx^3\]

We know that in that first ordered pair x = 4 and y = 16 so

\[16 = k\times4^3\]

A little simplification and we get

\[k = \frac{ 16 }{ 64 }\]

More simplified down we get

\[k = \frac{ 1 }{ 4 }\]

So now that we have what 'k' equals...we can figure out what 'y' equals in that 2nd ordered pair

\[y = kx^3\]

plug in everything we know

\[y = \frac{ 1 }{ 4 }\times2^3\]

What does 'y' equal...?

Answer 2

Y=2?

Answer 3

That would be correct!

Answer 4

Thank you so much!

Answer 5

No problem!