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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