Notes
This specification is referenced in the documentation of HelpfulEquation, HelpfulEquationNode,
SlopeInterceptEquation and SlopeInterceptEquationNode. To understand those types, you'll want to be familiar with
this specification.
The "helpful" format was arrived at via consensus at design meetings. It is PhET-specific, and does not correspond to a standard mathematical format. The intent is to create a clear association with the functions that are in the builder, and provide a "bridge" to the slope-intercept format. The term "helpful" is (thankfully) never shown to the sim user.
The "slope-intercept" format is the standard y = mx + b format, where m = rise/run and b is the y intercept.
Cards show the right-hand side of the slope-intercept equation. Eg, if the slope-intercept form is y = 2x + 2, then
the "x" card in the input carousel will show 2x + 2 in the output carousel.
Square brackets '[ ]' shown in the examples will not be rendered. They are used to indicate a numerator in this
specification. The forward slash '/' shown in the examples will be rendered as a horizontal line separating numerator
and denominator. For example, '[x + 3]/2' is rendered as:
![renderedEquation] (https://cloud.githubusercontent.com/assets/3046552/17148758/9daaa994-5325-11e6-9ccc-89f86e369d2a.png)
Examples
| Builder | Helpful | Slope-intercept |
|---|---|---|
| - 3 - 2 | y = x - 5 | y = x - 5 |
| + 1 - 2 | y = x - 1 | y = x - 1 |
| + 3 * 2 | y = 2(x + 3) | y = 2x + 6 |
| * 2 + 3 | y = 2x + 3 | y = 2x + 3 |
| * 0 * 2 | y = 0x | y = 0 |
| / 3 + 2 | y = x/3 + 2 | y = 1/3 x + 2 |
| + 2 / 3 | y = [x + 2]/3 | y = 1/3 x + 2/3 |
| / 3 * 3 | y = 3(x/3) | y = x |
| / -3 * 3 | y = 3(x/-3) | y = -x |
| / 3 * 0 | y = 0(x/3) | y = 0 |
| / 3 * 1 | y = 1(x/3) | y = 1/3 x |
| / 3 * 2 | y = 2(x/3) | y = 2/3 x |
| / 1 + 2 | y = x/1 + 2 | y = x + 2 |
| * 0 / 3 | y = [0x]/3 | y = 0 |
| * 1 / 3 | y = [1x]/3 | y = 1/3 x |
| * 2 / 3 | y = [2x]/3 | y = 2/3 x |
| - 3 * 2 + 1 | y = 2(x - 3) + 1 | y = 2x - 5 |
| - 3 + 1 * 2 | y = 2(x - 2) | y = 2x - 4 |
| * 0 * 2 + 1 | y = 0x + 1 | y = 1 |
| * 0 + 1 * 2 | y = 2(0x + 1) | y = 2 |
| * 1 * 2 + 1 | y = 2x + 1 | y = 2x + 1 |
| * 1 + 1 * 2 | y = 2(1x + 1) | y = 2x + 2 |
| * 3 * 2 + 1 | y = 6x + 1 | y = 6x + 1 |
| * 3 + 1 * 2 | y = 2(3x + 1) | y = 6x + 2 |
| / 1 * 2 + 1 | y = 2(x/1) + 1 | y = 2x + 1 |
| / 1 + 1 * 2 | y = 2(x/1 + 1) | y = 2x + 2 |
| / 3 * 2 + 1 | y = 2(x/3) + 1 | y = 2/3 x + 1 |
| / 3 + 1 * 2 | y = 2(x/3 + 1) | y = 2/3 x + 2 |
| * 2 + 1 / 3 | y = [2x + 1]/3 | y = 2/3 x + 1/3 |
| + 1 * 2 / 3 | y = [2(x + 1)]/3 | y = 2/3 x + 2/3 |
| / 3 + 3 / 2 | y = [x/3 + 3]/2 | y = 1/6 x + 3/2 |
Rules
Rules for generating "helpful" format:
(1) Adjacent addition and subtraction operations are collapsed, e.g.: + 3 - 2 → x + 1. If they collapse to zero, then
the operations are dropped entirely, e.g.: * 2 + 3 - 3 → 2x
(2) Adjacent multiplication operations are collapsed, e.g.: * 2 * 3 → 6x.
(3) Multiplication by 1 is shown, e.g.: * 1 → 1x, + 2 * 1 → 1(x + 2)
(4) Multiplication by 0 is shown, e.g.: * 0 → 0x, + 2 * 0 → 0(x + 2)
(5) If the portion of the equation preceding multiplication contains one or more operators, then it is wrapped in
parentheses, e.g.: - 3 * 2 → 2(x-3)
(6) Adjacent division operations are collapsed, e.g.: / 3 / 2 → x/6
(7) Division by 1 is shown, e.g.: / 1 → x/1, * 2 / 1 → [2x]/1
(8) Division by 0 is not allowed.
(9) The portion of the equation preceding division is treated as a numerator, e.g.: + 1 / 3 → [x + 1]/3