It is known that x and y are related by the equation y=ax^3+bx where a and b are constants  A straight line graph is to be drawn on the grid with y/x on the vertical axis. State the variable which...

It is known that x and y are related by the equation y=ax^3+bx where a and b are constants 

A straight line graph is to be drawn on the grid with y/x on the vertical axis. State the variable which must be plotted on the horizontal axis 

How do I know what variable should be plotted on the missing axis? 

Asked on by kimmiek

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embizze | High School Teacher | (Level 1) Educator Emeritus

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We are given that x and y are related by `y=ax^3+bx ` where the parameters a and b are constant.

If we want to plot a straight line graph where the dependent variable is `y/x ` plotted on the vertical axis, what variable will be plotted along the horizontal axis?

`y=ax^3+bx `

`y=x(ax^2+b) `

`y/x=ax^2+b `

This is in the form y=mx+b; the graph is a straight line with slope m and y-intercept b, the independent variable is x and the dependent variable y.

So for `y/x=ax^2+b ` we have:

`y/x ` is the dependent variable as needed.

The slope is a.

The y-intercept is b.

The independent variable is `x^2 ` .

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The variable along the x-axis will be `x^2 `

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