Sunday, May 22, 2022

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. 


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