Thread: help with non-linear laws and plotting them

Hi folks,
I have struggled with this since this type of knowledge isn't included in math syllabus in my country. Hope you guys can clarify and give me general method to solve this type of exercise :-)
---
It is known that the variables x and y satisfy an equation of the form: (x+y)/(xy)=a
where a is a constant. The table below shows approximate experimental values of x and y:

x	2	3	4	5	6
y	3	2.5	1.8	1.6	1.5

However, one of the values of y has been wrongly recorded. Redefine the dependent and independent variables so that there is a linear relationship between them. Plot this straight-line graph, identify the incorrect value and estimate the value of a
---
I have learned from some sources and come to this far: (x+y)/(xy)= a => 1/x + 1/y = a => 1/y = -1/x + a, which satisfies the form Y=mX+c with (Y=1/y; m=-1; X=1/x; c=a)
The point is that how can I plot straight line graph with the statistics, likewise how to identify the incorrect value and estimate the value of a (could this be done without a graphic calculator).

Thank you so much

Hey kopklan.

Are you familiar with linear algebra? You could set up a matrix and reduce it to find which row is inconsistent and thus which is wrong.

Originally Posted by kopklan

Hi folks,
I have struggled with this since this type of knowledge isn't included in math syllabus in my country. Hope you guys can clarify and give me general method to solve this type of exercise :-)
---
It is known that the variables x and y satisfy an equation of the form: (x+y)/(xy)=a
where a is a constant. The table below shows approximate experimental values of x and y:

x	2	3	4	5	6
y	3	2.5	1.8	1.6	1.5

However, one of the values of y has been wrongly recorded. Redefine the dependent and independent variables so that there is a linear relationship between them. Plot this straight-line graph, identify the incorrect value and estimate the value of a
---
I have learned from some sources and come to this far: (x+y)/(xy)= a => 1/x + 1/y = a => 1/y = -1/x + a, which satisfies the form Y=mX+c with (Y=1/y; m=-1; X=1/x; c=a)
The point is that how can I plot straight line graph with the statistics, likewise how to identify the incorrect value and estimate the value of a (could this be done without a graphic calculator).

Thank you so much

Plot a graph of u=1/y against v=1/x, the points should fall close to a straight line (of slope -1) except for the one incorrectly recorded.

.

not much, could you explain further for me? and btw, how could I pick up the value of a from the statistics when each pair of x and y results in different value of a.
And is this straight line we plot a visual estimation of flexible accuracy? (its gradient may vary depending on each person's estimation I presume)
Thanks

Originally Posted by kopklan

not much, could you explain further for me? and btw, how could I pick up the value of a from the statistics when each pair of x and y results in different value of a.
And is this straight line we plot a visual estimation of flexible accuracy? (its gradient may vary depending on each person's estimation I presume)
Thanks

There is another way, put u=x+y and v=xy, (then the expected relation is u=av) then plot that data, a will be the slope of the line, and the bad point will be somewhat more obvious that with the other method.

CB