Finding the equation for a graph where y and x values are known

[MasterSplinter]

Hi everyone!

I'm trying to find the equation of a graph where both the y- and x-values are known.


y = (100(b-a))/a
x = 100 - (((a/b)^1.5) * 100)

You can plot in any number you want for a and b, but:

b > a

Also

a > 19

I have plotted several points in geogebra, and the graph is going to look like this:

However, I am still not able to find the eqation for the graph. Can anyone help me? (please show work)

PS: I hope this is the right forum. If not, please move it to where it belongs. I am not that familiar with english math terms.

 

[Deleted member 4993]

Hi everyone!

I'm trying to find the equation of a graph where both the y- and x-values are known.


y = (100(b-a))/a
x = 100 - (((a/b)^1.5) * 100)

You can plot in any number you want for a and b, but:

b > a

Also

a > 19

I have plotted several points in geogebra, and the graph is going to look like this:

However, I am still not able to find the eqation for the graph. Can anyone help me? (please show work)

PS: I hope this is the right forum. If not, please move it to where it belongs. I am not that familiar with english math terms.

y = (100(b-a))/a
x = 100 - (((a/b)^1.5) * 100)

(1 - x/100)^(-2/3) = b/a...................................edited

y = 100 ( b/a - 1)

continue.....

 

[MasterSplinter]

Thanks a lot! The graph now goes right through all of the points!

However I am not able to understand the progress from

y = (100(b-a))/a
x = 100 - (((a/b)^1.5) * 100)

to

(x/100 -1)^(-2/3) = b/a

y = 100 ( b/a - 1)

Anyone wanna explain the steps in detail?

 

[stapel]

I am not able to understand the progress from

y = (100(b-a))/a
x = 100 - (((a/b)^1.5) * 100)

to

(x/100 -1)^(-2/3) = b/a

y = 100 ( b/a - 1)

Anyone wanna explain the steps in detail?

We'll be glad to help you with the algebra, but first we'll need to see where you're getting stuck. Please reply showing your efforts so far. Thank you!

 

[MasterSplinter]

I might be all wrong but I will try

I am thinking that he wants to isolate a and b when he gets
(x/100 -1)^(-2/3) = b/a

I've tried to get towards that answer:

x = 100 – ((a/b)^1.5) * 100
x – 100 = - ((a/b)^1.5) * 100
(x – 100)/100 = -((a/b)^1.5)
(x - 100)/100 = - (a^1.5 / b^1.5)

Im not even sure if this is the right way to do it, but now Im stuck.

I also have problems understanding how

y = 100 ( b/a - 1)

I was able to switch b/a with (x/100 -1)^(-2/3), making me able to graph the equation (thanks to Subhotosh Khan), but I struggle to find what's in between.

 

[Deleted member 4993]

I also have problems understanding how

y = 100 ( b/a - 1)

I was able to switch b/a with (x/100 -1)^(-2/3), making me able to graph the equation (thanks to Subhotosh Khan), but I struggle to find what's in between.

y = (100(b-a))/a

\(\displaystyle \displaystyle{y = \frac{100(b-a)}{a}}\)


\(\displaystyle \displaystyle{y = 100\frac{b-a}{a}}\)


\(\displaystyle \displaystyle{y = 100\left[\frac{b}{a}-\frac{a}{a}\right]}\)


\(\displaystyle \displaystyle{y = 100\left[\frac{b}{a} -1\right]}\)

 

[Ishuda]

Hi everyone!

I'm trying to find the equation of a graph where both the y- and x-values are known.


y = (100(b-a))/a
x = 100 - (((a/b)^1.5) * 100)

You can plot in any number you want for a and b, but:

b > a

Also

a > 19

I have plotted several points in geogebra, and the graph is going to look like this:

However, I am still not able to find the eqation for the graph. Can anyone help me? (please show work)

PS: I hope this is the right forum. If not, please move it to where it belongs. I am not that familiar with english math terms.

y = (100(b-a)) / a = 100 (b/a - 1)
x = 100 - (((a/b)^1.5) * 100) = 100 [1 - (a/b)^3/2]
Letting t = a/b we can write the equations as
y = 100 ( t^-1 - 1 )
x = 100 ( 1 - t^3/2 )
Working on the 'x equation' we have
t = [Something]^2/3
Substituting that into the y equation we have
y = 100 [Something^-2/3 - 1]

EDIT: Oh, and notice that because of the limits placed on a and b, that t is limited which means x is very likely limited. If so, that limit should be included in the definition of y.

 

[MasterSplinter]

Thank you for the help everyone, and I almost understand everything now. I understand the y-ecuation now, but I still struggle with the end of the x-equation I have gotten a little further:


[FONT=Times New Roman, serif]x = 100 – ((a/b)^1.5) * 100[/FONT]
[FONT=Times New Roman, serif][/FONT][FONT=Times New Roman, serif]x/100 = 1 - (a/b)^3/2 divide both sides with 100 (and rewrite 1.5 to 3/2)
x/100 - 1 = -(a/b)^3/2 Subtract 1 from both sides
1 - x/100 = (a/b)^3/2 Multiply with -1
(1 - x/100)^(2/3) = a/b Raise both sides to the power of 2/3

However, I dont understand the last step. How do you get a/b to become b/a, and how does (2/3) become (-2/3)?
[/FONT]

 

[MasterSplinter]

Ah, I found it!

I forgot the rule saying that 1/a^m = a^-m

Thanks for all the help I got. I would never have figured this out without you!