*The Museum of HP Calculators*

#
Equation of Line Given Two Points

By bill duncan

This program is supplied without representation or warranty of any kind.
The author and The Museum of HP Calculators therefore assume no responsibility
and shall have no liability, consequential or otherwise, of any kind arising
from the use of this program material or any part thereof.

##
Description

I often need to interpolate on a straight line given two points. This is
easy on calculators with linear regression built-in such as the HP-27 or
HP-15C. Using Linear regression programs available for other machines such
as the HP-29C or HP-41C is possible, but overkill for the 90% of the time
where I am just interpolating using two known points.

This is a very simple routine which does not use any registers. It is called
with the two points on the stack and returns with the coefficients on the
stack. Thus it is callable as a subroutine as well.

Input: Output:
T = Y2 Y = A
Z = X2 X = B
Y = Y1
X = X1 Where: A = y intercept, B = slope

When the routine finishes, you can calculate a new "*Y*" given
"*X*" by keying in a value for X and
pressing: *** +**

##
Note

This routine also works well with the HP-41C and probably most other RPN
calculators.

##
Example

The temperature and winds aloft are given for every 3000 feet. You wish to
fly at an altitude of 5000ft and are given temperatures of 10C at 3000ft
and 4C at 6000 ft. At 3000ft the wind is 15 knots at 200 degrees. At 6000ft
the wind is 12 knots at 215 degrees. What is the likely temperature and winds
at the height you wish to fly? (Very simple for illustration.)

10 ENTER 3000 ENTER 4 ENTER 6000 GSB 3
5000 * +
Answer displayed is: 6 degrees
15 ENTER 3000 ENTER 12 ENTER 6000 GSB 3
5000 * +
Answer displayed is: 13 knots
200 ENTER 3000 ENTER 215 ENTER 6000 GSB 3
5000 * +
Answer displayed is: 210 degrees

##
HP-29C Listing

Short and sweet. It's redundant on the HP-15C, but I find it useful on both
the HP-29C and the HP-41. Could probably shorten it for the HP-41C, but why
bother? Can anyone shave anything off for the HP-29C?

01 15 13 03 LBL 3
02 21 x<>y
03 22 RDN
04 41 -
05 14 73 LASTx
06 21 x<>y
07 22 RDN
08 22 RDN
09 21 x<>y
10 41 -
11 14 73 LASTx
12 22 RDN
13 21 x<>y
14 71 /
15 31 ENTER
16 22 RDN
17 61 *
18 41 -
19 21 x<>y
20 15 12 RTN
21 13 03 GTO 3

$Id: line.html,v 1.5 2000/07/05 16:45:53 bduncan Exp $
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