Draw a Straight Line Graph from Curved Line y=85x^(-1)

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Discussion Overview

The discussion revolves around the mathematical relationship represented by the equation y=85x^(-1) and whether it can be used to create a straight line graph by plotting y against the inverse of x. The conversation explores concepts of proportionality and graphing techniques.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that since y=85x^(-1), y is proportional to 1 over x, implying the possibility of drawing a straight line graph.
  • Another participant challenges this by stating that the graph of the function itself is not a straight line, but rather a hyperbola.
  • A later reply clarifies that while the graph of y against x is not a straight line, plotting y against 1/x would yield a straight line graph.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of the graph. There is no consensus on the initial claim about drawing a straight line graph without specifying the transformation of the axes.

Contextual Notes

The discussion highlights the need for clarity in mathematical relationships and the importance of axis transformations when interpreting proportional relationships.

fatoomch
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Hi,

If I have a curved line of, say, y=85x^(-1) could I say that y is proportional to 1 over x?... and use this to draw a straight line graph?

Thanks
 
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Huh? The graph of this function is no straight line.
 
sorry if I'm not clear on this.

If A=pi r^2 then A is proportional to r^2 and you could draw a straight line graph of A against r^2

so if y = 85x^-1 wouldn't y be proportional to the inverse of x?... you could plot a straight line graph of y against the inverse of x?
 
You are correct.

What radou thought you meant was that the graph of y plotted against x is a straight line (which isn't true; of course it's a hyperbola). However, if you change the axes and plot y against 1/x, then you will obtain a straight line graph.
 

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