Converting a Line in Parametric Line to a Function Line

Converting a Line in Parametric Line to a Function Line 

From (x(t), y(t)) to y(x)

Express a line, presented in parametric form:

x = A * t + B

y = C * t + D

where A, B, C, and D are constants, and convert it to function form (y(x) or f(x)).

Here is one way to do this:

x = A * t + B

A * t = x - B

t = x / A - B / A

y = C * (x / A - B / A) + D

y = (C/A) * x - B*C/A + D

y = (C/A) * x + (D - B*C/A)

We know have a function in the slope-intercept form where:

slope = C/A

intercept = D - B*C/A

Casio fx-4000P Program:  Converting Parametric Lines to Functional Line

Size:  77 bytes

(line breaks added for readability)

"X=AT+B; A":

?→A:

"B":

?→B:

"Y=CT+D; C":

?→C:

"D":

?→D:

"SLOPE="⊿

C÷A→M⊿

"ITC="⊿

D-B×M→I

Examples

Graph screens are created by the Numworks emulator:  https://www.numworks.com/simulator/

Example 1:

x = 3 * t  - 4 

y = 2 * t + 8

A = 3, B = -4, C = 2, D = 8

Results:

SLOPE = 0.666666667

ITC = 10.66666667

Example 2:

x = -2 * t + 6

y = 4 * t + 3

A = -2, B = 6, C = 4, D = 3

Results:

SLOPE = -2

ITC = 15

Hope you find this useful.  Take care,

Eddie 

All original content copyright, © 2011-2022.  Edward Shore.   Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited.  This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author. 

TI-84 Plus CE: Fitting a Parametric Line

TI-84 Plus CE:  Fitting a Parametric Line

The program PARLIN attempts to fit a parametric line for a collection of points (x(t), y(t)) using the following equations:

x = a * t + b

y = c * t + d

where the independent variable is t.  The program also plots the estimated line and the scatter plot.  I decided to keep the correlation (r^2) separate, so we can tell how well the line fits both the x and y data. 

TI-84 Plus CE Program PARAM

Notes:

L1: list 1, [ 2nd ] [ 1 ]; L2: list 2, [ 2nd ] [ 2 ], etc.  X1T, Y1T are from the [ vars ], Y-VARS, Parametric submenu

[square] is from [2nd] [ y= ] (stat plot) , MARK submenu, option 1

Program:

Param

Input "T LIST: ",L1

Input "X LIST: ",L2

Input "Y LIST: ",L3

FnOff

PlotsOff

LinReg(ax+b) L1,L2

a→A:b→B:r²→E

"AT+B"→X1T

ClrHome

Disp "X = A*T + B"

Disp A

Disp B

Disp "CORR: "

Pause E

LinReg(ax+b) L1,L3

a→C:b→D:r²→F

"CT+D"→Y1T

ClrHome

Disp "Y = C*T + D"

Disp C

Disp D

Disp "CORR: "

Pause F

min(L1)-5→Tmin

max(L1)+5→Tmax

FnOn 1

PlotsOn 1

GraphColor(1,BLUE)

Plot1(Scatter,L2,L3, [square] ,ORANGE)

ZoomStat

(Obviously use the colors and makers you like.   If you are working with a monochrome TI-83/TI-84, ignore the color commands.)

You can also download the program here:

https://drive.google.com/open?id=0B7R8x9Yi26yGZ2FkTVNYV3o3cGc

Example 1

Fit the data to a parametric line:

T	X	Y
1	2.3	-3.0
2	2.8	-2.6
3	3.2	-2.3
4	3.7	-1.9
5	4.2	-1.6

Results:  

x = 0.47*t + 1.83 (r^2 ≈ 0.998)

y = 0.35*t – 3.33 (r^2 ≈ 0.997)

Example 2

Fit the data to a parametric line:

T	X	Y
1	-1.0	1.000
2	1.0	1.250
4	5.3	1.746
8	13.6	2.825
16	30.1	4.275

Results:

x = 2.075268817 * t – 3.066666667 (r^2 ≈ 0.99997)

y = 0.2196827957* t + 0.857166667 (r^2 ≈ 0.99145)

Eddie

This blog is property of Edward Shore, 2017.