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The inputs above will be hidden when the program finally gets launched. Currently, I am not hiding them even when you close the calculator. The purpose of the inputs is to help in debugging. This allows you to enter simple code on the calculator screen but the program translates the input to javascript math. Give it a try and see if you notice any obvious problems or have suggestions for improvements.
Direct, Inverse and Joint Variation Help
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Direct Variation

The relationship between two variables that vary directly is of the form  y = kx.

Example 1:   Given:  y = 2x
For:  x = 3,  y = 2•3 = 6
For:  x = 9,  y = 2•9 = 18
Note: x tripled, so y tripled.
Example 2:   Given:  y = kx
If:  y = 15 when x = 5
Then:  k = 3,  y = 3x
Note: k = y/x.
When two variables vary directly, they appear to move in unison; i.e. if one doubles the other doubles, if one triples the other triples.

The k factor is simply the relation, k = y/x, which means that y will have to change by the same multiple as x in order for k to remain as a constant.

If x increases by a factor of m, then y must increase by the same factor, m.

k = my = my = y
mx mx x

Inverse Variation

The relationship between two vaiables that vary inversely is of the form  y = k/x.

Example 3:   Given:  y = 16/x
For:  x = 4,  y = 16/4 = 4
For:  x = 8,  y = 16/8 = 2
Note: x doubled, so y halved.
Example 4:   Given:  y = k/x
If:  y = 3 when x = 5
Then:  k = 15,  y = 15/x
Note: k = xy.
When two variables vary inversely, they appear to move in opposite directions; i.e. if one doubles the other halves, if one quadruples the other quarters.

The k factor is simply the relation, k = xy, which means that y will have to change by the inverse of the multiplier of x in order for k to remain as a constant.

If x increases by a factor of m, then y must decrease by the same factor, m.

k = mx • y = mx • y = xy
m m

Joint Variation

The relationship between three or more variables that vary jointly is of the form  z = kxy.
Joint variation implies direct variation of multiple terms.

Example 5:   Given:  z = 3xy
For:  x = 2,  y = 3,  z = 3•2•3 = 18
For:  x = 4,  y = 6,  z = 3•4•6 = 72
Note: x & y doubled, so z quadrupled.
Example 6:   Given:  k = z/(xy)
If:  z = 40 when x = 2 & y = 5
Then:  k = 4,  z = 4xy
Note: k = z/(xy).
Hopefully, you can see that joint variation is very similar to the direct variation described above.  Note that the dependant variable, z is dependant upon the xy product, which means that if x were halved and y were doubled, z would remain unchanged because the resultant product would remain the same.
Joint and Inverse Variation

Whenever you hear that a relationship is joint between some variables and inverse with others, simply apply what you have learned above.

Any variable that varies jointly or directly with another variable stays in the numerator and any variable that varies inversely stays in the denominator.

Example 7:   Given:  d varies directly with a & b and inversely with c.
Then:  d = kab/c
Example 8:   Given:  z varies directly with x and inversely with the square of y.
Then:  z = kx/y²
Although, the terminology may become confusing at times, simply remember that direct variation results in equal affects and inverse variation results in opposite affects.  Joint variation, as you've just learned is just another term for direct variation.  Good Luck!

© 2002- John Schlecht. All rights reserved.