STEM PRACTICE AND EVIDENCE WORKBENCH
Derive rise, run, slope, and intercept from two points and audit learner parameters with unit-aware visual evidence.
Review output
Load the worked example to inspect realistic inputs, or enter anonymous classroom or laboratory evidence. Results remain in this browser tab until you copy or download them.
Transparent method
For points with x1 different from x2, rise equals y2 minus y1 and run equals x2 minus x1. Slope m equals rise divided by run. Intercept b equals y1 minus m times x1 and the intercept point is (0,b). Compare learner m and b separately with expected values using the declared relative percentage tolerance. Supported means both parameters agree for the two supplied points. Slope carries y units per x unit; intercept carries y units and represents the model at x zero. That value may be physically impossible or outside the domain. Review the graph, scale, residuals, measurement uncertainty, linearity, relevant interval, and contextual meaning before interpreting either parameter.
Confirm the learning question, authoritative source, units, notation, response coding, model assumptions, and review threshold. Keep an unchanged copy of the original evidence and remove learner names or identifiers.
Run the worked example first, inspect every intermediate row, and compare it with a hand calculation, diagram, representation, or approved subject method. Correct input evidence before interpreting a flag.
Record the method, assumptions, units, classifications, and flagged rows. Verify the editable report independently, connect the numerical signal with learner reasoning, and document any teaching or laboratory decision outside this tool.
How to interpret the result
Use when learners need to connect two points with rise over run, rate units, an equation parameter, and the intercept point. The table makes each intermediate quantity visible. It does not prove a relationship is linear, fit noisy data, infer causation, judge whether extrapolation is sensible, handle vertical lines, select axes, or replace a graph with its domain and uncertainty.
From (1,5) to (3,13), rise is 8 and run is 2, giving slope 4 and intercept 1. The cooling row has slope negative 2 and intercept 20. A horizontal row has zero slope and intercept 7. The final points give slope 3 and intercept 5, so learner values 5 and 3 are both flagged.
For points with x1 different from x2, rise equals y2 minus y1 and run equals x2 minus x1. Slope m equals rise divided by run. Intercept b equals y1 minus m times x1 and the intercept point is (0,b). Compare learner m and b separately with expected values using the declared relative percentage tolerance.
Supported means both parameters agree for the two supplied points. Slope carries y units per x unit; intercept carries y units and represents the model at x zero. That value may be physically impossible or outside the domain. Review the graph, scale, residuals, measurement uncertainty, linearity, relevant interval, and contextual meaning before interpreting either parameter.
Do not reverse rise without also reversing run, divide x change by y change, drop a negative sign, read the first y-value as intercept when x is not zero, force a vertical relation into slope-intercept form, omit units, or extrapolate automatically. Substitute both original points into y equals mx plus b and compare with a graph.
Learning boundary
This browser-local workbench applies only the disclosed rules. It cannot diagnose a learner, certify an experiment, establish assessment validity, or replace teacher, laboratory, curriculum, accessibility, and safety judgment.
Review checklist
Practical questions
No. Processing occurs in the current browser tab. Avoid personal information and retain authoritative records only in the approved school system.
No. It describes entered evidence under one disclosed rule. Review reasoning, uncertainty, access, and several evidence sources.
Treat it as an editable calculation aid. Show your own reasoning, cite required sources, and follow course and academic-integrity rules.
YOUR NIRMION
