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 


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