## 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

"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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