Before generation
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.
Worked example
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.
Formula or methodology
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.
How to interpret the result
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.
Common mistakes
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.