Topic 2 of 6
Linear Relationships
Read slope as a rate, build equations from data, and connect tables, graphs, and formulas without treating them as separate topics.
01Algebra · Concept explainerSlope is a rate of change, not just rise over runSlope measures how much the output changes for each one-unit change in the input. Its sign, size, and units all carry meaning.02Algebra · Method guideHow to write a line equation from two pointsFind the slope first, anchor it to either point, then convert forms only if the problem needs a different presentation.03Algebra · Decision guidePoint-slope or slope-intercept form: which should you use?Use point-slope form when a point and slope are given; use slope-intercept form when the intercept or a quick graph is the main goal.04Algebra · Concept explainerParallel and perpendicular slopes, with the vertical-line exceptionParallel nonvertical lines share a slope. Perpendicular nonvertical lines have slopes whose product is −1—but vertical and horizontal lines need separate language.05Algebra · Direct answerWhat do slope and intercept mean in a linear model?The intercept is the modeled output at input zero; the slope is the predicted change in output per unit of input. Context decides whether either interpretation is sensible.