Straight line graph

Question

A straight line graph obtained by ploting y/x against x² .The variables x and y are related by the equation y = -1/4x³ + 9/2x. Find the value of a and of b.

V(a,5)

W(6,b)

Answer 1

Hi Octavia N.,

Sorry but you haven't quite put together a question there. It's true that for the stated y=f(x) function, a plot of y/x vs. x^2 will yield a straight line:

original y = -(1/4)x^3 + (9/2)x

then y/x = -(1/4)x^2 + 9/2 , and that describes a straight line for (y/x) vs. x^2.

But, what are points V and W to us? Are they points on the original graph of y vs. x?

Or are they points on the graph of y/x vs. x^2?

It makes a difference -- if one coordinate is x^2, you can take the square root, plug it into the y(x) equation, and get a y. But if it is just x, then you plug it into the y(x) equation as is.

Try it both ways, just to impress your instructor ....

--Cheers, --Mr. d.