My Math Forum a curve to a straight line

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 April 11th, 2016, 02:52 AM #1 Newbie   Joined: Apr 2016 From: england Posts: 19 Thanks: 0 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.
 April 11th, 2016, 02:58 AM #2 Senior Member   Joined: Jun 2015 From: England Posts: 853 Thanks: 258 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? Thanks from waynebutt
 April 11th, 2016, 03:09 AM #3 Newbie   Joined: Apr 2016 From: england Posts: 19 Thanks: 0 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
 April 11th, 2016, 03:31 AM #4 Newbie   Joined: Apr 2016 From: england Posts: 19 Thanks: 0 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
 April 11th, 2016, 03:36 AM #5 Newbie   Joined: Apr 2016 From: england Posts: 19 Thanks: 0 I did this as a straight line for non linear equations
April 11th, 2016, 04:00 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, 04:07 AM #7 Newbie   Joined: Apr 2016 From: england Posts: 19 Thanks: 0 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
April 11th, 2016, 04:12 AM   #8
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Quote:
 Originally Posted by waynebutt 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

 April 11th, 2016, 04:15 AM #9 Newbie   Joined: Apr 2016 From: england Posts: 19 Thanks: 0 thanks there is no negative values but good to point that out when I write it up thankyou
 April 11th, 2016, 05:32 AM #10 Senior Member   Joined: Jun 2015 From: England Posts: 853 Thanks: 258 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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