📖 4. Graphs

📖 From Digital SAT Algebra • 270 questions available

About 4. Graphs

Graphs provide a visual way to understand and solve algebraic relationships, transforming abstract equations into pictures that reveal patterns and connections. This chapter begins with the rectangular coordinate system, also known as the Cartesian plane, explaining how to plot ordered pairs (x, y) and identify the four quadrants. Students will learn to find solutions to linear equations by creating tables of values, and then use those points to graph linear equations by plotting and connecting them. The chapter also covers intercepts—where a line crosses the x‑axis and y‑axis—and teaches the slope of a line as a measure of steepness, including how to calculate slope from two points and how to interpret positive, negative, zero, and undefined slopes.

Moving to applications, the chapter introduces the slope-intercept form (y = mx + b) and the point-slope form, showing how to write equations of lines from given information such as a slope and a point, or two points. Students will learn to graph horizontal and vertical lines, and to find the equation of a line parallel or perpendicular to another line. The chapter also explores graphing linear inequalities in two variables, including how to shade the correct half-plane and use solid or dashed boundary lines. Finally, the concept of relations and functions is introduced, using the vertical line test to determine whether a graph represents a function. By the end, students will see graphs not just as pictures, but as powerful tools for modeling real-world situations like distance, cost, and growth over time.

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🔄 Last updated: 2026-09-07