Unit 7 Summary

Pre-Algebra · Axiom Academy

SUMMARY The Coordinate Plane & Linear Relationships A recap of how a constant rate of change becomes a straight line — and how slope, equation forms, and systems let us model real situations. Linear means a constant rate of change. When equal steps in x always produce equal steps in y , the graph is a straight line. Slope is that rate. It measures steepness as — how much y changes for each unit change in x . One line, several forms. Slope-intercept, point-slope, and standard form all describe the same line; pick whichever fits the information you have. A system is two lines at once. Its solution is the point that satisfies both — geometrically, where the lines cross. Graphs make the pattern visible and turn many word problems into a picture you can read. Core Concept The Coordinate Plane A grid that locates any point with two numbers, written as an ordered pair (x, y) — x horizontal, y vertical. The two axes split the plane into four quadrants, and every point that satisfies an equation can be plotted. Order matters: (3, 5) and (5, 3) are different points. Watch out for: a linear equation plots as a straight line — every solution lies on it. Core Concept Slope (Rate of Change) Positive rises left-to-right; negative falls. Zero slope = horizontal line; undefined slope = vertical line. Core Concept Forms of a Linear Equation Every line can be written several ways — each one the same line, just convenient for a different task.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.