Core Math & Algebra
One page, four essential algebra helpers: solve linear equations, solve quadratics, find slope and line equation, and evaluate a point on a line. Built to match Common Core algebra topics.
Solve linear equation (ax + b = c)
Core Algebra Formulas
1. Linear equations
ax + b = c → x = (c − b)/a, with a ≠ 0.
2. Slope-intercept form
y = mx + b where m is the slope and b is the y-intercept.
3. Quadratic formula
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
If the discriminant D = b² − 4ac is:
- positive → two real solutions
- zero → one real (double) solution
- negative → two complex solutions
4. Slope from points
m = \frac{y_2 - y_1}{x_2 - x_1}
Formula (LaTeX) + variables + units
This section shows the formulas used by the calculator engine, plus variable definitions and units.
Formula (extracted LaTeX)
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Formula (extracted text)
ax + b = c → x = (c − b)/a, with a ≠ 0.
Formula (extracted text)
y = mx + b where m is the slope and b is the y-intercept.
Formula (extracted text)
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Formula (extracted text)
m = \frac{y_2 - y_1}{x_2 - x_1}
Variables and units
- No variables provided in audit spec.
Sources (authoritative):
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Changelog
Version: 0.1.0-draft
Last code update: 2026-01-19
Last code update: 2026-01-19
0.1.0-draft · 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.