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April 11th, 2016, 03:52 AM   #1
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Question a curve to a straight line

hi there I currently have a problem I cant seem to solve

y=ax^2/b

now the questions asks

Imagine that you have been given a series of values for x and corresponding values for y. If you plot y against x your graph will not be a straight line. What graph of y or a term involving y against x or a term involving x could you plot to give a straight line? Note: This part of the question has more than one correct answer, but you are only required to give one of them.?

can anyone point me in the right direction please
preferably and example that's not like this question so I understand the concept here.
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April 11th, 2016, 03:58 AM   #2
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First of all, why not let c = a/b to make the equation easier?

Now, have you heard of change of variable by substitution?

What would happen if you let


$\displaystyle X = {x^2}$

and plotted y against cX?
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April 11th, 2016, 04:09 AM   #3
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the question is really would that give a straight line or would the answer still come out as a curve ?

I can do variable substitution which I overlooked to be honest.

thanks
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April 11th, 2016, 04:31 AM   #4
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this is what I did

y = a x^2/b
y/x^2 = a/b
x^2= a/by

x^2=a/b y

comparisement with y=mx+c or y = kx

gradient =a/b

a= gradient/b
b= a/gradient
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April 11th, 2016, 04:36 AM   #5
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I did this as a straight line for non linear equations
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April 11th, 2016, 05:00 AM   #6
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As I see it, the question only makes sense if you already know x and y.

That is you are working on a table of results or measurements from some physical experiment etc.

So if I let my c = 1 to remove the constants altogether.

Here is a table of such results, what do I get if I plot x^2 against y or y against x^2?
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April 11th, 2016, 05:07 AM   #7
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your a genius buddy thanks that is what ive been looking for

so if a/b =1

then the x and y coordinates would match up so the imputed value of x would ultimately be the corresponding value of y


so reall its like y is y^2 as the numbers match
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April 11th, 2016, 05:12 AM   #8
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Math Focus: Wibbly wobbly timey-wimey stuff.
Quote:
Originally Posted by waynebutt View Post
your a genius buddy thanks that is what ive been looking for

so if a/b =1

then the x and y coordinates would match up so the imputed value of x would ultimately be the corresponding value of y


so reall its like y is y^2 as the numbers match
One thing to be careful of. The linear graph studiot suggested isn't quite the same as the general equation of a line. If we have the line y = x, for example, if the domain is all real numbers the range will be all real numbers. But if you plot y = x^2 (y vs x^2) as studiot suggested then if the domain is all real numbers you will find that the range is all positive real numbers. ie. the negative y values do not appear in the graph of the line.

-Dan
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April 11th, 2016, 05:15 AM   #9
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thanks

there is no negative values but good to point that out when I write it up

thankyou
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April 11th, 2016, 06:32 AM   #10
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Of course it also depends upon what you mean by plot.

As I noted, you have to know both x and y to draw the line on ordinary graph paper, so I don't see a domain issue there.

If you only know x to start with, there is no straight line that you can draw connecting x and a non linear function.

You can, of course also use non linear axes such as log paper to achieve the straight line objective, but you still have to know x and y to make the plot.

However, I did wonder, if you were studying nomograms?
With these you would connect suitable non linear axes with straight lines, to read off y, geven x, (as well as a and b).
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